Cheaper? maybe in the short run. DO NOT make the mistake of buying a car that has modifications unless you know they are done right. When I got my car it was already lowered. I've spent more money correcting the suspensions issues because he did it wrong. The camber was way off so I would go through tires all the time. It would be a lot better and a lot more interesting for you to buy a stock car and build it up. You would learn a lot more that way as well. If you want something fast, look at the B18C1 (GS-R). It's a nice engine and has a lot of potential. I'm not just saying this because it's what I have, it really is a nice engine. Some people might say either LS/VTEC or B18C5 or B18C (Type R USDM and JDM) but they cost a lot more and takes more work for little gain.
It's hard to say where to start from though. Anything anyone says is usually an opinion of what they want. any car with a B18C1 (GS-R) would be quick, reliable, and you only have to do regular maintenance on it. If you get that engine (in any Honda), you have the potential to later build it up and make a pretty fast car.
I don't know. What you want to do and spend is really up to you. My vote is for a B18C1 in whatever car you like the look of best. That's just me though.