Don't underrate the 22.
From bench testing over 100 makes and models, most 22 rifles are well capable of popping bunnies at 100 if shot in properly with their preferred ammos. Rifle price is often an indicator of quality, but not necessarily of accuracy. Some comparatively cheap 22s will shoot under 1" groups at 100m, and a $247 Norinco EM332 I had with a huntsman 3-9x AVERAGED 0.6" for four consecutive groups at 100m. I have no trouble popping sub 1" groups with quite a few makes eg marlin bolts/semiautos and JW15s - and that means very dead bunnies at 100m.
The right ammo for your 100 meter shooting is the ammo that shoots best off the bench after testing 8-12 different types through any given rifle. Sporter rifles will often shoot just as well with the right high velocity ammo as they will with subs (excluding match ammos here). Here's some pics of just 2-3 standard barrel 22s off the bench - absolute sharpshooters, cheap as chips (all under $250) and with inexpensive optics:
Three .22 sharpshooters
You can choose to spend up on a 22, but in fact you don't need a $600 scope plus $1000 rifle. Just pick one of the good accurate rifles, pop a reliable scope on it and spend some good bench setup time.
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