I know lots of little girls who wouldn't be comfortable with a Handi-weight 243. That's a fair amount of recoil for a small child.
The recoil my friend would entirely depend on the load choosen..Saying the 243 kicks a-lot is exceedingly strange to me..Many are recomending using a pistol cartridge..For each of what has been mentioned..I am quite sure I can find a hard kicker in those if I choose to..
Take a look at a Lyman reloading book..a 84 grain cast bullet at 1605fps..kicks less than some factory 223 loads..
Jacketed bullets...lots of info out there for reduced loads as well...
Any rifle I have ever set up or helped set up for a small child..has always had a soft cheek piece on it..and a great recoil pad..Has always been fitted to the child using it..Have always made sure the child had the best ear plugs and ear muffs along with safety glasses..Doing this will reduce not only the felt recoil to them..but will reduce the majority of percieved recoil they experiance..
The 243 isn't a bad choice..you just have to set it up for the child..not yourself..
Mac