Do you have any regs to min caliber of airgun required?
What distance do you call accept your longest shot to be? But, a powerful .45 Caliber with a good HollowPoint will do the job. Personally I like the Extreme.457 with a Robert Vougal 280HP or a RJ Porter 310gr HP For a scope a Vortex Diamond Back 4-12-40 with hash marks work great. The AOA .45 Bushbuck- TEXAN .45 - Quackenbush .45 and a very others are great choices for deer. Matter of preference, which ever set up you pick practice and find your most accurate ammo. Remember SHOT PLACEMENT is KING! Best of luck Brother Man
Budget ?....There's plenty options out there, budget will help dictate what direction to loot at.
175 - 200 yds is out of the question...You have to liken big game hunting with an air rifle to bowhunting. Meaning, you have to get close... Not quite as close as a bow hunter has to get but, close. IMHO, 80 yds and in...80 yds being the absolute maximum distance....Here is the choice I made: http://www.rlairgunsupply.com/Texan-Shrouded-Combo-RL-Airgun-Supply