I'm putting the finishing touches on my house design, and I'm trying to figure out the best way to go on my HVAC duct work. I have 3 options (that I know of).

1) Duct work in the basement. The air handler will be in the basement regardless. The house will be in SC, and I know from local experience that the un-conditioned basement will be about 55 for a winter low, and 75 for a summer high. A little asset for the A/C, a little loss for the heat. Basement ducts mean floor registers. I don't know which is better- floor registers or ceiling registers, or if the difference is significant. Floor registers are a pain due to furniture placement, though.

2) Duct work in a dropped ceiling. I could either build the whole house with a dropped ceiling, or just certain areas. The central 'core' of the house has closets, bathrooms, and halls, all of which could have a dropped ceiling. The registers in the main rooms could be the upper wall. I specifically do not want a separate chase, as it would look odd in a vintage style of home. Here in FL, it's traditional to put ductwork in the super-hot attic- I'm not gonna do that, either.

3) Mini-splits. The house is essentially 3 rooms, not including halls, closets, and bathrooms. Having separate mini-splits could be a potential savings with good thermostat management.

The house will be one story, 1250 sq ft, built over a walk-out basement (possibly ICF). Construction will likely be 2X6 framed walls with foam on the outside for a thermal break, cellulose in the walls, and careful attention paid to sealing everything. Attic will be R-38 or so. I'm currently trying to decide if the extra cost of ICF walls will pay off in the mild climate. We tend to follow the seasons, with the thermostat around 60 in the winter, and 80 in the summer. We turn off the HVAC and open the windows in any kind of tolerable weather. What do you think is my best approach?

If you insulate your basement walls including the band joist & foundation sill your wintertime lows will be in the 60s, and in summer it'll be pretty much the same temp you keep the first floor.  In SC (US climate zone 3) there's a long-term financial argument for insulating basement walls to R10 or so, even putting R5 under the slab.    That would be 2.5" of unfaced EPS (bead-board)  or 2" of XPS (pink, blue, green, grey, doesn't matter) on the walls, 1" of XPS (or 1.5" of EPS) under the slab.  On the wall-EPS you can seal the seams with 1-part foam, then put in vertical furring through-screwed into the concrete for hanging the code-required gypsum.  Then 3" of open cell foam (or 2" of closed cell, if you use one of the DIY-kits)  can be used to seal the foundation sill & band joist to the EPS.  Vertical furring through-screwed to the concrete can then be used to hang the interior gypsum (required by code for an ignition barrier.)  If a termite barrier is required, use the thinnest copper flashing underneath the foundation sill, extending in beyond the interior face of the wall foam. 

Alternatively going with ICF for the foundation may not be dramatically more cost than an interior-side-only skin using virgin-stock sheet EPS, and with ICF you start at R16.  If you use new EPS on the wall R10 will run you about a buck a square foot. XPS is usually a little more.  But reclaimed EPS from commercial building re-roofing or demolition runs about 30 cents per square foot, at which point even 3-4" thick R12-R16 is cost-effective, bringing it up to 50-60 cents/foot.  (You may have to call around to find a source, but they're out there.)

At SC subsoil temps the additional heating/cooling load of fully conditioning an insulated basement is miniscule, and it improves the indoor air quality by elimiating seasonal mold-potential on the joists, etc.   With an insulated slab inside of conditioned space you can even leave a cardboard box on the floor without much risk of mold, whereas in an unconditioned basement in SC the summertime humidity creates mold & mildew issues with just about any organic material in the basement, giving anything you store down there the "musty basement" smell, or worse.

There's also an argument for R50 attics too, if you do it with cheap stuff like blown cellulose. Ponder the first chapter of this document, and refer to Table 0.2 p.10 for some guidance on R-values.

A 2x6 wall with cellulose fill and an inch of exterior iso is R20, so you're already at their guidelines on that.  A minimal ICF wall is R16, but the up-charge for going to R20-R22 isn't much.  The energy benefits of ICF are pretty marginal compared to R20-whole-wall stick built, but in hurricane zones there's a structural/survivebilty argument for going that route.

R410A mini/multi-splits are generally more efficient than ducted systems, and are cost-effective in heating mode too.  Rather than 3 seperate units, there are a few 2-2.5 ton VERY efficient Mitsubishi & Daikin models that take up to 3 separately controlled interior units- you can micro-zone it. (At 3 tons + you get more heads, but somewhat lower efficiency.)  See the bottom portion of this document for some 2 & 3 head multi-split models.  It's a moving target- I'm sure Fujitsu & Samsung et al either already have similar models that would work, or will 20 minutes into the future. With inverter-drive compressors you can pretty much set & forget them- the modulate with the load and run very efficiently.  If you get into set backs or frequent temperature changes up/down etc the fact that they turn the compressors faster during recovery means they deliver lower average performance than if you'd left the temp alone. (The lower loads of setbacks are larger than the efficiency hit during recovery.)  Many mini-splits also have a "dehumidify" mode, which is useful when you have only a latent load and essentially no sensible load (which will be fairly often in the spring & fall if you go with R50 roof and R20 walls.)  Just be sure to make provisions for disposing of the condensate.

Getting your heating & cooling loads down at that point is a matter of  optimizing (mostly reducing) the glazed area  & type, using insulated doors, etc. 
With R20 clear-wall R values  even a pretty-good U0.34 window begins to dominate the heat gain/loss of a 8'x12' section of wall if it's more than 12.5 square feet:

12.5 x0.34= 4.25 BTU/hr/degree-F

The entire is 8x12= 96 square feet, less 12.5' of window leaves 83.5' of insulated wall:

83.5 x 1/20= 4.18 BTU/hr/degree-F

Even small reductions in glazed area matter!

Swinging patio doors provide more cross-sectional area for your walk-out basement than sliders per amount of glazed area, and they seal better too (especially long-term.) Casements & awning windows seal better than double-hungs, and provide more egress area and ventilation cross section per square foot of glazing too. Fixed windows for daylighting-only seal even better.

Dana- Thanks for the excellent reply!

This build will largely be DIY, and on a tight budget as well. I know a good ICF guy in the area that will work with me. I can stack the block and do the bucks and bracing, and he will inspect it and do the pour (for a fee). It will be somewhat cheaper than paying someone to do it all. The only problem I have with ICF is that I will then have to put up drywall in the basement, and apply a finish over the outside, whereas with a poured foundation, I can just leave it as-is, and finish the basement at a later time. Time and money are important factors.

We are in the Upstate area, nearly into NC, and well out of hurricane zones. We're 15 miles, and higher elevation than the nearest city. It is about 5 degrees cooler on a hot summer day than the city is, and it's amazing the effect being in or near the woods has, too. We'll have a decent wood stove for fun, power black-outs, and the once-a-decade night that gets down near zero. We'll be able to use the wood stove quite a bit, as I have an endless supply of wood, but as I get older, I will lose the ability (and desire) to cut, stack, and haul wood.

It is noteworthy that a conditioned basement offers very little extra load than duct loss to an "unconditioned" basement.
Heat is not delivered as comfortably from the top down, though cool air loves it.
All systems have there drawbacks, but in my neck of the woods, the ducts would be in the basement.
j

If ducted, no doubt the basement is the location. But air handler power adds up, cutting into the net efficiency, and ducted systems (even well-designed to manual-D and with well-sealed ducts) create pressure differences between rooms, which drives outdoor air infiltration and adding somewhat to the load, none of which happens with split-systems.

Outdoor temps as low as 0F are not a problem for most mini-splits. Mitsubishi Hyper Heating spit systems specify 100% of rated heating output at +4F, and will deliver over 70% of the rated output at -13F, but below that all bets are off. Most of the Daikin heating/cooling mini-splits are similarly designed to be able to operate wall into negative digits. I'm not sure where the lower limits for Fujitsu units are, but there are quite a few in service in my area, with design temps a few degrees either side of 0F. At 0F the COP on any of them is a bit under 2.0, but at mid compressor speeds most will deliver a COP of 2.5 or better at +15F, and 3.0 or better at +32F. Assuming your climate is more like Asheville or Henderson NC (with 97.5% design temps of 14-15F) you'll likely be in the ~3.0 range for a heating-seasonal average using a split system.

We're warmer than Asheville, which is about 50 miles away, but 1000 feet higher in elevation. I would say on average 5 degrees warmer. Our closest city is Greenville, SC. How do I find the design temps for Greenville?

google:

"outside design temperature" greenville sc

(include the quotation marks)

When you find several references with design temps that differ by a few degrees, the lower temp is usually the 99% ASHRAE number, the higher one is the 97.5% number. Either is suitable for sizing the heating/cooling on a standard code-min house, but at higher R (and higher interior thermal mass) even the 97.5% number is more appropriate.

The 97.5th percentile heating design temp for Greenville SC is +22F. (A temp at which mini-splits are running a COP of 2.8 or better at mid compressor speed.)

The 99th percentile design temp for Greenville SC is +18F.

So I suppose your "...on average 5 degrees warmer..." estimate was right on the money.