You have quite a few possibilities for rifles within the $700 range. I do have to agree with anthonyg and refer you to the CZ452. You cannot go wrong with it, it will even give you money leftover for a scope and good rings and bases. The are very accurate and easily customized when it comes to tuning the trigger.
Stay away from the 597, you can customize them a bit, but the triggers are hard to maintain and they have issues ejecting and loading. Half of them are not even worth the potmetal they are made out of. For that matter, I wouldn't waste any money on the 10/22.
I you are stuck on shooting an automatic you might want to look at Briley
http://www.briley.com/. However, if you are just starting out, I really think that you would be better served with a bolt action rifle. I would stay away from the 77/22 because of the accuracy and trigger issues they have. If you keep your eye out you may find a Remington 541-S that may be good.
For the $700, I think that you would be best served with a used hunter silhouette rifle. I think that you could find a Kimber, Sako, or even an Anschutz if you were patient. I would start asking the guys at the matches, I am sure that someone is selling a hunter gun in that group.
In reality most of the American made firearms require a lot of work/cost to make them accurate and reliable. The europeans really own the nitch right now with the CZ, Sako, and Anschutz.
Casey