243s do the trick, but are limited in penetration without premium bullets, so being picky about your shots is critical, for this reason alone I think of the 243 as more of an experienced rifleman's cartrage. 30-30s have superb penetration but are lackluster in their external ballistics so getting close to your target is vital, also a skill of crafty veterans. Faster 30 cals tend to be a bit harder kicking and are not the cartrage of choice for new recoil shy shooters, keep it under 15lbs recoil for a new shooter. I think the ideal beginners gun would have to be in the .257-.284cal range capable of 2700fps+ speeds to ensure flat trajectory and ideal shot placement within reasonable ranges. 25-06, 257 Roberts, 6.5x55, 260 Rem, 6.5 Creedmore, 7mm-08 and 7x57 would top my list. If someone is capable of a little more recoil I could make a strong case for the 308 and 270 win too.
As someone who reloads I prefer the 6.5x55, 120gr bullets at 3000 fps and sissy kicker recoil, think of it as 270 win lite. But if I used factory fodder I would probably prefer the 25-06 or 7mm-08.