As others have mentioned, take a safety course. It can only do you good.
In that price range you definitely have some options to get you started. In a lever action, you could look at Marlin for sure. If you don't mind used, check into a Winchester Model 94.
In bolt action, definitely check into a Marlin XS7 or XL7. Supposedly great rifles that perform well above their price point. Add a $150-$200 scope and you're well under your $700 limit.
You could also consider a package such as the Remington ADL 700 at around $550 (price in my area), though I'm not to sure those package scopes are the best way to go. You can also find packages from Savage Axis, the T/C Venture and Weatherby Vanguard.
Best thing to do is visit a local shop and chat the owner or employees, someone should be able to steer you in a good direction. Handle a few options and decide what feels right and fits you best.
As far as caliber, in a lever action the .30-30 is THE iconic standard. In a bolt, I feel that .243 is a good start if recoil is an issue, otherwise the .270 is really hard to beat for sheer versatility without stepping up to a .30-06 level of recoil, plus it can be loaded down for varmint. (Yes, I am a huge fan of the .270. When I got back into firearms after a long absence and could only afford ONE gun, I went .270)
Good luck and have fun!
You can take the Texan out of Texas, but you can't take Texas out of the Texan.