If just for deer, than any one of the myriad of short action cartridges, including the 243 Win, 260 Rem, 6.5 Creedmoor, 7mm-08 Rem, 308 Win, 338 Federal or 358 Win in a bolt or lever action will work just fine out to 250 yards, where they will still retain a minimum of 1000 ft lbs of energy. You could also add the 257 Roberts, 25 Creedmoor, and 6mm (Rem or Creedmoor).
In long action cartridges, the suggestions of the 6.5x55 and 7x57 (AKA 275 Rigby) are also good choices.
While deer do not necessarily require larger calibers or heavier bullets, the effectiveness of 30 caliber bullets of 180 grains, and larger/heavier, has long put game on the tables of families. They do provide a margin of additional mass and momentum that cannot be denied in their ability to provide quick, clean kills, when bullets are placed accurately. I have used most of the cartridges above to take deer and other big game over the years, and am particularly fond of the 6.5s (Creedmoor and Swede), 338 Federal and 358 Win.
In the brush, where your long shots are going to be out to 250 yards, a short, handy bolt action, or a lever action such as the Browning BLR, Savage Model 99 or Winchester Model 88 in any of the cartridges listed above are great choices. Henry even offers some of the non-traditional lever action cartridges in some of their rifle models. While most people may think of levers as short range firearms, there are several capable of reaching out further than one might think.
It will depend upon your preference as whether you prefer a bolt action or a lever action rifle.
Then it will depend upon which cartridge you prefer, and its availability in the rifle you prefer.
Best of luck in your quest!
