A PSE Phaser II was my first bow. I think it was a 100 dollars set up new. I killed a bunch of deer with it but man it is a different world now. That bow had very little let off and was slow but it proved to me that you do not have to have a 1500 dollar set up to kill a deer.
Just about any modern bow now is going to be such a huge step up that you will be pleased with about any of them. I have had a good number of bows since my first one and some were better than others but every one would kill a deer.
If you can shoot some and get a feel for them. I shoot a Mathews Q2 that I bought in 2002 and still love the way it shoots. Speed IS NOT the most important thing. Get one that has a good smooth draw and is forgiving. Most speed bows are less forgiving and less accurate unless your form is very good and most times more noisy. Just about any bow you find will be much faster than that Phaser however. Good luck.