If you want something that is cheap but accurate it is hard to go wrong with an Axis. They may not be pretty, they may not have the best fit and finish, but they're damn accurate. And relatively light too.
I had a 783 for a short while and on mine (in 7rem mag) it was a bit picky with feeding. For some reason if you only loaded 2 rounds in the mag it jammed on the 2nd round every time. Only 1 round or a full mag and it wasn't an issue. Didn't keep the rifle long enough to figure out the problem, sold it to buy a left-hand hunting rifle.
I also wasn't a big fan of the stock on the 783. Felt chunky in the hand, for lack of a better term. Maybe thats a plus for some, but it wasn't for me.
I don't think you can go wrong with either of these options, they both meet the goal of affordable and accurate... Ruger American might be worth looking at too, especially because you can run AR mags in them with an adapter IIRC.