I like the
Cape Cod and Saltbox style. The important thing about keeping building costs down is the KISS formula -- Keep it simple, stupid!
(Nothing personal. It's just a saying.)
Rule #1: Check your local bylaws. A friend of mine had to take off a little guest room he built over his garage. Expensive waste!
Rule #2. Have a simple design. Avoid 'pointy things' on your roof. Gables and skylights are tricky to build well, so they make your construction labor costs balloon, and there are problems -- leaks, particularly -- that follow as the night follows the day.
Idea #3. Consider a crawl space instead of a full basement.
Idea #4. Don't skimp on insulation or double-paned windows. It will save money later on - a lot.
Windows.Idea #5. A 2-storey (or even a 1 1/2 storey) house is cheaper to build than a bungalow.
(Edited later in view of MrsS's excellent (as usual) post:
Usually erecting a house to "lockup" stage costs about 1/3 of the total cost of an average 'stick' house -- frame structure. "Lockup" is sub-floor, roof, walls, doors and windows. After that comes wiring, plumbing, insulation, drywall, ceiling, painting and flooring, and built-in storage (kitchen, bathroom, bedrooms).
You need professionals to build to 'lockup', but you can do a lot of the other stuff yourself. Here we are even allowed to do our own wiring -- but it must be inspected before we can turn the power on. The one not to do yourself is plumbing, imo.
If you do your own insulation, be sure to get a good 'handyman' book to guide you. A lot of people make the mistake of putting the vapor barrier on the wrong side of the insulation, with nasty and expensive consequences.
And drywall takes a lot of skill. If you decide to DIY, don't use gypsum board. Use something with a texture -- it's more forgiving.