heres my suggestion. Pick up a quality short action rifle like a rem model 7. Something thats light and compact. The 243, 260, 708 and 308 will all work but for an 8 year old girl all 4 are pushing the limit in recoil to allow her to have fun shooting it. What i would do is pick any of the above and load up some light loads using cast bullets and slowly work her up to level that would work on deer. even with jacketed bullets a 308 for example can be brought down to fairly mild levels of recoil with say a 130 grian bullet at 2000-2500 fps and still do well on deer out to a 100 yards. Worse mistake people make with kids is starting them with full power loads. even a 243 that doesnt have alot of recoil still has enough muzzle blast to startle a child and make them want to quit. Sits some pop cans out with some pop gun loads and let them have fun for a summer before you get serious with them.