It's been a few years since I've played with a .243 (not much call for it in NC), but I've owned and shot them on and off for 32 years now.
I've generally preferred 87 gr BTHP or V-Max on prairie dogs mostly due to improved wind bucking over a lighter, faster bullet with a lower BC. At 400 yards you'll get about 8" of drift in a 10 mph full valve cross wind with an 87 gr BTHP or V-max compared to about 12" with an 75-80 grain bullet or 10" with a 65 grain V-Max bullet. And despite the differences in velocity (3200, 3400 and 3700 fps), with a 350 yard zero the point blank ranges are all plus or minus 5 yards of 400 yards. In other words, they all shoot equally flat past about 300 yards.
For coyotes, there are two schools of thought - use an FMJ and get clean entry and exit holes, or use a varmint type bullet that will over expand and fragment leaving a clean entry hole and (hopefully) no exit holes. My preference has always been the FMJ as the performance is consistent and effective even at long range, while the SX type bullets would often leave several holes on the exit side on shorter range shots. But I may be in the minority here.
On white tails and particularly antelope where the ranges can be longer, way back in the day I preferred the 87 gr BTSP because at long ranges it gained ground on the 100 gr SP in terms of energy and trajectory (although I still preferred the 100 gr bullet on mule deer). However the 87 gr BTSP has been discontinued and a 100 gr BTSP is available and it now retains energy much better. It's a little sad though as an 87 gr BTSP would do anything from varmints to smaller deer and antelope and do it pretty well.
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Powder wise, I usually stay with IMR 4895 or 4064 on the 80 and 87 grain bullets and stay with IMR 4831 on the 100 grain bullets. Those powders let you get good load density and peak velocities with very good accuracy (in my rifles at least). They are extruded powders and don't meter quite as well as a ball powder (especially 4831), but I don't mind throwing an undersized charge and trickling up to the weight.