Assuming that your daughter has had some experience and is really ready for a centerfire, I think that the .243 suggestion is a good one. Anything lighter/smaller will not go the distance, anything heavier will either beat her or have to be built too heavy to be handy.
The 6mm will render slightly better velocities , especially with heavier bullets, and will also render more recoil. The .243 is much more common, data abounds, and .243 cases are available by everyone, including Lapua.
I had GAP put together a .243 for my own 21yo daughter, based on a Remington LTR. The only difference being that the LTR comes with a 20" barrel and we installed a 24" Schneider. With the OEM LTR stock, Farrell rings & bases, Leupold 4.5-14x PR and Eagle stock pack, it weighs 10.5#. I also have a spare PSS stock, which I have on it now, since it raises the comb a little for her.
She uses her's for long range target shooting. She attended a very challenging tactical match with me in May, and the rifle shot very well for her (placed 18 of 29).
For truly long range shooting, you're going to have better results with the heavier bullets. David Tubb markets a proprietary .243/115 grain Sierra Match King, called the "DTAC", that shoots extremely well and has a BC of about .585.
I got slightly flatter trajectories and excellent accuracy with Lapua 105 Scenars. They don't quite have the BC of the DTAC, but can be driven 175-200 fps faster in the same cartridge and shoot bugholes. I have 105 Bergers on hand, but I think that they'll be too long to seat to mag length and still shoot well.