If you do a lot of prairie dog hunting, I would not recommend the 243. It is somewhat of overkill for the small critters. A 223 is a good choice, especially if you do not handload, becuase of CHEAP ammo. A 22-250 is also a good choice especially for long range shooting. A 223 is also a good round for coyote hunting, but you cannot take really long shots, unless you are confident in your shootin skills. For what you are looking for, I would recommend the 204. It shoots jsut as far as a 22-250 with less wind resistance due to its design, plus it is a little more accurate. It has plenty of power for coyotes also. The 204 also uses less powder than a 22-250, so barrel life is better.
As far as barrel choices go, it depends on if you do a lot of walking. If you do, I would just go with a medium barrel in probably a 24" version. If you do not walk much, buy a heavy barrel, or even a heavy fluted barrel becuase they are more accurate, and do not heat up as fast. If you do a lot of prairie dog hunting, use the heavy barrel because one tends to shoot a lot, and you will not want to heat up your barrel becuase it is damaging to the rifiling. I hunt yotes, fox, and prairie dogs, and I use a heavy 26" barrel 204 because it suits my style of hunting. plus the accuracy of the 204 is unbeatable by ANY round.