Don't waste your time with the 770 Remington and just pony up the money for a 700. You will have more options to upgrade later if you want a new trigger, optics mounts, or stock. Plus if you ever want to change out the barrel IIRC you throw away the 770 and buy a different rifle.
Now if you want a rifle to get you though a season or two until your money situation improves then look at a Stevens 200 or the Marlin XL/XS rifles. The run about the same price point as the 770 and are better rifles IMO. When you want to upgrade later you will be able to sell them for a much better price than any 770 Remington.
Cartridge choices I'd look at depends on what your intentions with the rifle are. Pretty much the .243 Win, .270 Win, .308 Win, or .30-06 are great places to start if you are talking a hunting rifle. All will handle deer sized game quite well and not break the bank to shoot. If you are talking target rifles then I'd look towards the .223 Rem and .308 Win, the .223 will be the cheaper of the two to shoot.