The best advice I can give you is to go to a few pro shops and shoot a few within your price range. They have new bows set up for just this purpose, and if not, they normally don't have a problem setting up any bow you'd like to shoot. Mathews makes an awesome bow (and is what I shoot), but the price generally keeps a lot of people away. You won't need top-shelf equipment to have fun, but if the archery bug grows enough, you'll end up there eventually. One good/bad thing about bows is that they don't hold their resale value very well (unlike firearms, for example). If a new bow costs $900 (bare) this year, it can probably be found next year for around $600-700 or less, and it will continue to get cheaper as time progresses.
For example, the last bow I purchased was a 2005 Mathews Switchback. New, it retailed for around $800, and I picked it up in 2008 for $400 shipped...and that included a decent arrow rest and some usable sights. If you already have a brand or model of bow in mind, a good place to shop for a used bow is archerytalk.com. There's TONS of great deals in their classified section. Sponsored archers generally get their bows for free, and sometimes they even get more than one per season. Those bows often end up for sale if they like the bow they currently shoot versus a new one. Also, a lot of people think that they need the latest and greatest. So, when the bow companies release their new models (once per year), they'll sell off their like-new bow from last season to get the new model; often at a substantial loss.