I JUST went through this whole process! Just got my first pin almost 3 weeks ago. I started out with a budget of $1,700, but ended up spending $2,500 for a HUO Rollercoaster Tycoon, and it was DEFINITELY the right decision. Here's some advice from my experience (some of it will echo what has been said already).
1. Follow the aforementioned advice and go play every game you possibly can! My wife and I went around for months following the Pin Map on this site playing every machine we could get our hands on. We found a lot of machines that we really liked, but more importantly we found a lot of machines that we thought we'd like, but we really didn't. In the end we ended up going back to the same place over and over and spending hours on end drinking beer and playing Rollercoaster Tycoon. Through the natural process of playing everything we could, that became the game that we wanted. A lot of people told us it sucks, but for us, this was definitely our pin for number 1, so don't put any stock in other people's opinions, because they are just that...opinions.
2. Once you decide which 1, 2, or 3 it is that you want, decide that you're going to spend on the top side of the curve for that machine and be patient until you find the right one. We waited and waited until we were frustrated, but in the end the right one popped up eventually. My RCT is GORGEOUS and it's been so much fun having it in the house. Having a beautiful machine has given me the opportunity to just start customizing, not repairing. Plus, it's your first pin. You WILL want to show it off and have people over. Having a pinball machine of your own is ridiculously cool, and for the first one, it's just the best move to have one you can proudly display!
3. Buy from a trusted Pinsider if you can. A great percentage (but obviously not all) of people who care enough to participate with this forum also care enough to take great care of their games and also to care about their reputation.
Just my $1.25 on the subject. If you take no other advice...just load up the pinmap and start playing!!!