Any of the rifles mentioned are just fine.
The 243 is a great tweener cartridge. It shoots fast, flat and, with 100 grain bullets, pretty hard. It is the top of the list of good varment calibers and the bottom of the list of good deer rounds. It doesn't kick much, so is a great rifle for a young person just learning how to shoot center fire. It is also a good choice for a woman (or a man for that matter) who is afraid of a .30 kick. If I had a teenager I wanted to give one center fire, I would probably choose a 243 --actually I would prefer to give him or her a 6 MM Rem (which is really a .244 Remington with better ballistics than the 243) but that round has been sent to the dust bin of marketing history. It is a good 300 yard rifle, but beyond 300 yards its punch drops off dramatically.
In my state of Missouri about 10% of all deer hunters use a 243, which I have always found really surprising since most hunters will claim the 243 isn't big enough for deer. A lot of others claim that it isn't much of a brush gun and Missouri is a state with a lot of woods type hunting. What it is really good for is hunting out of a tree stand over a modest sized field, so that is probably why it is popular with a lot of hunters.