Ditto on DannyD's advice. 243 is preaty sweet for a first rifle. Ive seen alot of youngins use 410's with slugs also. You could get a Rossi 410/22lr combo gun for $150ish and would be a good starter rifle. I think starting with a single shot or only 1 round in the gun is a good idea. I know to many expericenced hunters that are more worried about a quick 2nd shot on a deer then a good 1st, if you only have 1 then it has to be a good shot. I think if they started out with just one shot they would have a different attitude towards shooting.

An Encore is a nice 1st rifle if you dont really have a budget. They get kinda pricey with more then one barrel and scopes and stuff. Model 7 or a Browning Micro Hunter(my fav) are also good rifle choices.