>>828001All posts below you will find people recommending a proper .22LR rifle, 10-22/Marlin/Bolt action all good picks but not 1:1 comparison to AR7.
If you would like a rifle that packs in a floating water-tight case that takes little space in a bag or strapped outside the bag; the AR7 is your pick.
If you want to walk around with a 'proper rifle' that means added weight and likely 1-2 hands preoccupied. Depending on your terrain/distance/skill this could be a game changer, personally I carry the AR7 when I plan to hunt small game; if there is a chance for waterfowl/bird I will bring 410/22; if there is chance for bigger game hog/deer I will bring a proper caliber to match the game hunted.
If you have 0 firearms and this will be your first; a bolt action 22LR is good (Marlin recommended but not the only brand) but I would recommend Henry Rifles in the desired caliber. Lever action with wood furniture from a quality manufacturer just does not get much better.
Henry/Browning/Rossi for lever rifles; Browning might be better quality but owning BLRs and Henrys I favor tube magazine over cartridge.
Back to the question of OP; AR7 would work well for your task, any firearm will honestly even an M4 22LR. .22LR Lever action/Bolt action/AR7/Over-Under/Even 20gauge and up shotguns would be what I would recommend selecting from.
Even further, if you honestly are not familiar with firearms and only plan to hunt rabbit/squirrel/varmint with; you could get an air rifle to save weight and costs.
I own the AR7, a BLR, Marlin bolt, a few Henry lever rifles, and Chiappa over/under double badger. If I do a multi-day trip it easily would be the over/under. If I were to go out for a day of hunting small game I would take my Henry 22 lever over my AR7 or Marlin 22 bolt. The AR7 would be more desired if I were on a kayak/canoe trip and worried about water but wanted to hunt small game. I do not use my Marlin bolt anymore, but it damn sure is accurate and sexy.