You will likely not match .22LR energy levels (typically 40 grain or slightly lower projectile weights, and 11-1200 FPS muzzle velocities. Although those are subsonic, they are actually in the transsonic velocity range. For your consideration: Diablo-shaped pellets (the vast majority of the normal, skirted pellets used in airguns) are inherently unstable at transsonic speeds. Air rifles can be as accurate or more accurate that .22LR firearms at short ranges, but energy and accuracy will be directly proportional to cost.
If you are looking to shoot 100 yds accurately with an air rifle AND want reasonable terminal energy, you might consider shooting slugs (bullet-shaped projectiles). The heaviest .22 cal pellets top out about 25 grains. You can find good slugs at that same weight or heavier, and they are more stable at higher velocities (so better for longer ranges). Obviously, heavier and faster also translates to more downrange energy. Also obviously, to push heavy projectiles faster, you need a "stronger" airgun. These do get pricy. FX has an excellent reputation, and several of their rifles offer barrels designed for slugs. They are not the only game in town, and there are a number of high quality rifles available from other manufacturers. Another consideration for the longer range, higher impact energy equation is larger calibers. You might look into rifles in .25, .30 or larger calibers as well.
To put your toe in the water, I might suggest that you compromise on range and energy, but definitely try a PCP. Something like a Benjamin Marauder in .22 or .25 caliber would give you a feel for a decent PCP and keep you in the $500 range (you will also need some form of high-pressure pump to charge the rifle). Can shoot further, but best accuracy at 50 yds or less. Better rifles (such as Air Arms, Daystate, FX, RAW, etc.) will run you closer to $1500-$2000+, and will require an electric pump to keep them charged up.
Good luck, hope some of this is helpful.
