First warrior, let's get something straight: there is no such thing as an affordable M14. :lol:
With that out of the way, we can discuss a few things...
The cheapest M14s are the Chinese variety. A Polytech M14 will command about $800 these days on the low end, and push $900+ on the high end. The stocks suck and the bolts are soft, and other than metric threading on the gas system parts (which isn't a bad thing, just a minor pain in the ass), they're great rifles. Even Ron Smith and Clint McKee, who both are in the business of telling you whatever they need to get you to buy their stuff, admit that Chinese receivers are the closest thing to having a USGI M14 receiver as you can get without having a USGI M14 receiver. Other parts, the barrel in particular, are as good as or superior to USGI parts, and most of the parts are superior to Springfield Armory, Inc. parts (Chinese op rods are one piece forged and harder than SAI op rods, for example).
Long story short: a Chinese M14 with a USGI bolt conversion will be an amazing rifle that will last a lifetime. Just be sure to buy Chinese gas system parts as spares because the metric threading will cause problems if you try to make a repair with an American part that uses Imperial threading.
Springfield Armory, Inc. rifles are, in general, pretty low quality compared to a real USGI M14. The receivers are cast in Canada instead of forged, other parts are cast or of lower quality and tolerances, and so forth. The rate of failures for SAI guns tends to be pretty high; a cursory glance through technical threads on the M14 forums will prove this. However, unlike the Chinese guns, SAI has a lifetime transferable warranty. No matter what happens, no matter if you're the original owner or not, as long as the problem wasn't your fault, SAI will fix your gun or replace it outright. That's pretty awesome no matter how you look at it.
Long story short: SAI M1A/M14s are good rifles but they're nothing like the real deal. They're materially different and dimensionally different, but they are guaranteed forever. I personally recommend buying a used one, both because new SAIs are way too damn expensive, and because of the transferable warranty. Let someone else break the rifle in and discover any problems it has, then reap the benefit of paying less for a proven rifle.
Then you have Fulton Armory guns, Smith guns built on LRB receivers, etc. I wont bother discussing these rifles because you said "affordable." M14s from these guys are anything but affordable.
So you're really left with two choices: a Chinese gun that needs a USGI bolt conversion, or a SAI gun that isn't technically as good as the Chinese guns, but may indeed shoot and function great, and has a warranty and superb customer service backing it up.
If I didn't already have two M14s that I scored amazing deals on and was starting from scratch, I'd buy a used SAI M14. With Chinese M14s approaching $1,000, it doesn't make any sense at all to buy a gun that you know beforehand needs work only to pay in the end what you would have spent on a SAI M14 that was already good to go.
A year or two ago when the Chinese rifles were $500-$600, I would have told you the opposite.
Right now, MedCpt has a brand new
SAI for sale for $1,300. I'd be talking to him if I were you.