I kind of understand the draw of the Remington 783, being so cheap.. But if you plan on building a precision rifle you may as well invest the extra couple hundred bucks to start off with to get a nice action..
Personally, I'd get a t3x in 6.5 Creed. It will shoot lights out stock, and when funds allow you can put it into an MDT chassis. The triggers are excellent, the action is glassy smooth. The MDT chassis takes standard AICS mags, which you can get in 5, 10 or 12 round varieties which MDT makes also.
I have a t3x Varmint in the ESS chassis. Stock barrel and trigger, but it shoots like a laser and there is no reason for me to upgrade..
Take a gander through the "Show me your factory tikka groups" thread on here if you have any doubts.. These guns are tack drivers.