Just curious on how you will cut the logs to lumber dimensions?
Will the lumber require inspection so it will meet specifications for your building code?
There are a number of small portable planers on the market. These will work but most only go to a maximum of 13 inches and usually cost maybe $600 dollars and down in the Canadian market.
The next step up planers have larger beds and usually start at about 15 inches wide and up. These will have 220 volt higher horsepower motors and are quite durable.
I have one of the cheapest portable planers, a Delta. 12 inches wide, two reversible blades. You do get snipe with it on the planed boards. Mine is set up so there is a six foot in feed and out feed table. It has planed many boards and has produced a lot of shavings. The drive pulley on it has required replacement.
For house building quantity lumber I'd recommend a commercial milling operation for cutting and finishing the logs to lumber. Constant thickness and square edges may be a problem for the "do it yourself" concept. Also the wider board edges may not be planable or it would be difficult to plane them.
For some portions of house building unplanned lumber may be used. " Code's"
Note: I very much enjoy planning lumber. For me it's fascinating.
Attached is a picture showing my planer set up. It may not look all that great but it does work.