You can, there's nothing that prohibits giving primary instruction in an experimental, you just can't get paid for it. The bigger issues are: 1) most though not all experimentals are unsuitable as primary trainers...even RVs, though they're well-mannered for high performance airplanes, are still high performance airplanes I wouldn't turn a 10-hour student loose in 2) finding an examiner qualified and willing to give a PPL checkride in your type can be difficult.

Sailingfun is 1000% correct that the initial purchase price is a relatively small portion of aircraft ownership...however, most other costs go up with speed, capability, and complexity. It's worthwhile to really hone in on your ideal mission. If it's really training and knocking around in the local area, a two-seater will save significant money in gas, insurance, and maintenance over a typical four-seater (which is really a three-seater unless both rear-seaters are kids). Fixed gear saves a lot of insurance and maintenance money over a retractable gear airplane, at the cost of x/c speed and fuel economy. Taildraggers are more fun than trikes but cost more to insure, especially once you throw a student pilot on your insurance. Etc.

For an economical but relatively fast and fun two-seat trainer, I'd suggest looking at the Grumman AA1A Traveler series. Same fuel burn as a C152 but about 20 knots faster, not much higher purchase price, and rather RV4-like handling.