If you haven't operated an LAA aircraft before then I would suggest getting a share.
That will allow you to see what's involved. For your 20-30K you should get a share in an RV. This should also be easily to sell if you should decide that you want to go in a different direction (aerobatics, vintage, open cockpit etc).
If you want to do quite a bit of touring then I would suggest that 120kts + should be a requirement and also a fairly high wing loading as this will reduce the bouncing around from turbulence.
Some of the very efficient LAA aircraft do achieve this with very low wing loadings and are not so comfortable in turbulence.