Hey There, My wife has bad allergies/asthma/breathing problems, you name it she probably has it. We are redoing a house completely and was thinking about heating options that are both efficient and not terribly expensive. I was thinking of installing a wood stove, and then supplementing that with electronic baseboard heating around the house. I was hoping that by not having forced air, it would cut out on having allergens and dust being blown around. I know baseboard heating isnt as pretty and it gets in the way of furniture, and it wont match our 1908 farm house that we are redoing, but im just trying to think of ways to not have to use gas/oil and no HVAC. I dont think I can afford to put in a boiler system in the house. Any advice on electronic baseboard heating would be greatly appreciated. Thanks! (also constructive criticism in my logic and plans its greatly appreciated as well)

A woodstove is the totally wrong solution for better air quality. Burning any solid fuel in the house will release large quantities of particulates, some of which will get into the air and on your walls and ceilings.
Where are you and what are the thermal conditions (insulation & infiltration values) of your house?

I have a wife with similar issues that can be quite severe. You won't want to hear this but the absolute best system would be radiant heat in the floor. Retrofitting an old farmhouse could be prohibitively expensive though. I concur that you do NOT want to do a wood stove for the reasons Bob noted. Baseboard radiation (hydronic) is not horrible but it has to be kept meticulously clean - meaning vacuuming every 4 - 6 weeks during the heating season. Forced air would be the last choice.
Regardless of what you do for heating I recommend you install central vacuum system with an exhaust piped to the exterior. We have found that to be the single most effective change we have made in terms of respiratory issues.

Good luck!

I second Birman's recommendation of the central vac. We've had one for 35 years and I'm always surprised that clients aren't interested. Not hard to install yourself.

A sealed combustion-direct vent water heater with a sub-system for radiant floor, walls and ceilings.

If the envelope is tight enough and the loads reasonable a combi-water heater would be ideal.

If you must use electric as I do, then an electric boiler with electric Marathon water heater would work, as it doe for me.

We also burn wood and have the requisite Energy Recovery Ventilator (HEPA is available), since the cleanest environment will not be for long.

If you know how to burn solid fuels and have the proper equipment air quality need not suffer. If you have a critical reaction to the byproducts of combustion, cracked heat exchangers give me an instant headache, then a wood boiler must go outside.

Unfortunately there are no cheap solutions to acute sensitivity.

I have baseboard electric heat. It works OK and it's very expensive. I installed radiant heat in a new shop that I built and it's fantastic. So much so that we are retrofitting out 100 year old house with radiant heat. You might get some prices for radiant and compare it to the electric baseboard.

I'd also keep the house very dry and use very good filtration in the HRV system.