Guide to a Budget m16-type DMR:
Buy a cheap used Full length M16/URX/SR16 etc. Free float handguard, one piece or high quality two-piece outer barrel is a must. You might have to upgrade to this if you can't find it on the gun of your choosing
Replace the hopup unit, bucking, and nub. (I like king arms units, g&g green buckings, and element h nubs)
Replace the barrel with a tb (I have had good experience with the AirsoftGI Brand 6.01)
Get higher rate of spring. (Guarder SP130 or higher for real DMR performance)
Buy some HIGH quality BBs, mid-heavyweight (.28-.36).
Make sure the gears are shimmed perfectly, and your piston is in good shape. The cylinder head, piston head/oring, and the nozzle all need to be high quality and in good shape to ensure repeatable fps.
You'll probably need to upgrade gears/motor/battery/piston/gearbox and move to solid bushings if you go much above a 130.
Finally, sorbothane pads on the cylinder head can help adjust AoE and reduce stress on the gearbox and also quiet down the whole system.
Chances are, $250 isn't going to get you to a DMR-class weapon. Especially if you start with a new gun instead of used.
Guide to a cheap and fairly accurate gun:
Get a dboys/cyma/kalash AK with a full length outer barrel (New or used)
Get a M120 or SP110 spring, bearing spring guide, and a modify polycarb piston, and piston head.
Get an airseal nozzle.
Get a new hopup bucking and nub (Once again, I love the G&G greens + Element H nubs)
Get a tightbore (Madbull 6.03's work great for this when you're on a tight budget).
Easy to do under $250, but won't get you looooong distance. Just above average distance.