In an effort to keep your costs as managable as possible I would suggest that you start with the biggest engine that you can shoehorn into your frame.
That is the exact opposite of what you want to do. Find out what mods need to be done to each engine to meet your goal and pick what is in your price range. Building a high horsepower 390
is not cheap. Everything for bigger engines costs more. An animal or GX200 would probably be best imo if you want to keep the costs down. A good example of this is a GX200 piston is $19 at NR-racing right now. They don't make GX390 flat top pistons, so you need to buy a Honda probably about $25 if I remember then have the dish machined out which will cost you more.
Hydraulic brake setups go from $150-$200 plus all the parts for the live axle, bearings, sprockets. So your looking at about $250-$300 just for a live axle set up, if you want the best.
If you go to a taller than a 6" Kart wheel that will also cost more. You would be looking at a Jr drag wheel and tire, which is probably around $125.
Machine work will all add up, also.
All in all, you need to have a budget in mind. A definite speed, 55-70 is a huge range and can mean a big difference in cash. Are you going to ride it around? If so, alcohol is probably not an option, it is tough to have the engine idle a long period of time running on alcohol and burns much more fuel.