Re: 243 for long range?
The 70 gr Nosler Ballistic Tip, 80 Gr Sierra Blitz, and Hornady 87 gr VMax are all awesome coyote/groundhog bullets in a .243. The 87 Vmax is very capable of going to 1000+ with great accuracy. I have a bud who has several PD kills over 1000 yards with that bullet.
There are a lot of good target bullets in the 95-107 gr range to shoot paper, and a few may even work well for deer to 500. Sierra, BIB, Berger, Precision Ballistics to name a few. You just need to make sure the rifling twist is fast enough for bullets over 100 gr.