This was one of the most helpful and informative replies I've seen on this board. Thank you Sir for your effort.It is easy to get caught up and confused with the variety of 7.62 rifles out there. I am fortunate that I have one of each so will give you a quick rundown that may help you.
CETME/HK/Clones. Good overall guns if you can handle and inspect them first or have a working knowledge of them so when you get it you can identify any flaws. I have a CETME with HK internals which shoots and works wonderfully. Mags are cheap, accesories are common, again just have to watch and fit accessories carefully some fit better than others.
Cost is well within your budget, generally brass it flung far and wide and is damaged beyond use on occasion so reloading may be out. Optics are easy to mount with the claw mounts or other systems. Reloading mags into the weapon straight in with a push button mag release mags generally drop free.
FN/FAL and clones. Overall fantastic rifles just have to watch where you get them from. I have a L1A1 that has a lower from the Aussie Defence Force, 1962, with a century receiver. You just have to make sure they are headspaced correctly which most are. I prefer the L1A1 series because they will accept either inch or metric mags. Others will only accept metric mags.
Mags in general are cheap and they will shoot pretty much any ammo and optics are easy to mount by replacing the top cover. Mags are rocked into place from the front to back depending on model has a mag release lever two handed reloading here mostly.
AR-10's are nothing more that stretched out AR-15's with refinements. Most external accessories made for the M4 type rifles will work on them. Internals are different. Most are very accurate but heavy at times. Mags depending on the brand of rifle can be common FN mags or proprietory to the gun and very pricey.
Optics are easy to mount, most rifles come with a rail system. I prefer RRA just because of the triggers I have seen and shot some AR-10's that the triggers are horrible. Most of the time you can order with your choice of barrel length and twist rate to suit your needs. Mags go straight in and push button release mags generally fall out themselves.
M1A family. From the days when battle rifles were made of wood and steel. I have an M1A made in late 2001 with some of the last GI parts and a 1963 TRW barrel on it. Love the rifle. Very accurate and reliable mags can range from new Checkmate Ind. mags to cheap surplus.
Owners will range from out of the box goes bang is fine with me to every part must be GI spec and matching to get the utmost out of the rifle. I am middle of the road I guess my rifle shoots fine for me have added a few aftermarket parts to make it shoot better and more reliable.
Mounting optics is not a cheap deal on this rifle. Avoid SA mounts and optics they are more trouble than they are worth. Mounts can be from cheap to just plain damn expensive. You can order a surplus mount for $35 and fight it all the way or get a Sadlak Titanium for $400 and put it on and forget it. Once optics are mounted you will need a cheekpiece to bring your eye in line with the optic these can be lace on leather or ones you actually attach to the stock.
Surplus stocks can range from cheap beat up ones to new fangled aerospace plastic and aluminum for over a grand just for the basic stock. Mags are rocked into place has a mag release lever you have to practice to become proficent with the reloads.
You can get into a CETME, FN well within your budget and buy all sorts of goodies for it including optics. The AR-10 you can get the rifle and stay under budget but optics and such may have to wait. You can still find M1A's in your price range but have to look hard and jump when you find it. You did not say if there is a specific job you will want the rifle to do defense, long range shooting, hunting or so on. Just decide what the main duty the rifle will be used for and choose one that will meet your criteria.
Hope it helped and didnt add to the confusion.