CH, If the govt. won't allow any calibre larger than the .270 (actual .277), that would seem to be your best choice. A 7mm (.284) would be too big. A .270 with a lighter bullet would do well on coyotes and such, while the 150g is fine for deer and bl. bear.
Be sure to include a scope and rings in your budget. Without good glass, your rifle won't be that useful. You should plan on spending as much for your scope as your rifle to really get a good shooter. Savage with their new trigger would be a good choice as they are very accurate and still inexpensive. Don't buy the package with a scope as the scope is not of good quality. You'll have to spend quite a bit more to get any better performance than the Savage offers.
The long and short trajectory is a new one on me. Try getting actual catalogs from the rifle makers as well as some ammo makers. That should explain all you want to know about trajectories. If not, try the library for books on shooting and ballistics. Good luck.