The 25.06 is a great rifle for her

Recoil:
A 25.06 weighing 8 lbs(scope included) with a 120 gr bullet travels at 2950 fps and free recoil energy of 14.5 .lbs..Would be probabless less with factory ammo.
In comparison a 257 roberts(same rifle weight and same bullet weight) travels at 2775 fps....Recoil 11.4 lbs

My suggestion would be let her try a 25.06 or similar cal and see what she thinks.

Oh Ya! Watch that scope comming back and hurting/cutting her. Many a person got split open by scope recoil and younger folks have a habbit of not holding firearm tight and snug enough and tend to "creep into the scope"

Of the three choices I would say a 7-08 but, I would suggest you put her into a 260 rem. Extremely accurate round. Light on recoil and a good selection of bullets from target to small game to large, deer size game out to 300ish yds.

If the elk can be thrown out of the equation, I'd go with the 243. If not probably the 7mm-08. At this stage in the game she'll have the most fun with the least recoil, so some light varmint loads in the 243 would be the way to go, then work up to the 100 grain.

If after a few years she wants to bust elk, then trade the gun in for something more powerful.

...what he said

yeah I probably should stick with what I know. I killed lots of critters with my old .243. I also killed 6 elk with that .243. But, I won't make this a "is or isn't the .243 big enough for elk" thread.

I just am wanting a caliber that can grow with her. I'd like to load light loads for her to use at the bench and on varmints and also be able to load it heavier for bigger game. Does anyone think a 25-06 or 7mm-08 can be loaded light enough to have recoil comparable or less than the .243? She's spending a lot of her own money on this rifle and wants to keep it a long time.

Handloading, you can brew up some lighter, reduced loads but, I don't recall ever seeing any light, over the counter, 7-08 or 25-06 loads.
If she's looking to purchase her own first rifle. Take her out shooting. See what she likes. She may surprise you and pick one that you thought was more than she can handle. Then again, as young as she is. The 243 would be a more comfortable, all day shooter and a round that she could use for many years.

yeah I'd have to buy factory loads and shoot them myself then neck -size and reload the lighter loads. I prefer that to buying brass. She likes the feel of the new savages and shoots a lot but there is no place around here with lots of different calibers to shoot. She's shot .243 before and liked it. She didn't like my .308 at all but it's a light lever gun (it got sold anyways) and I won't let her try the .300 win yet. I have an old mauser chambered in .300sav that I'm workin on but she doesn't like the feel of that rifle.

I think we decided she's gonna have a NEF Handi-rifle in .243. Then, when the time comes to hunt elk, we spend a hundred and change on a new barrel. How does that sound?

Follow up question: is neck sizing instead of full case sizing a problem for single shot rifles?
thanks

That is an interesting decision on the rifle choice. I have a two barrel NEF set up that I like to take on backpack hunts. I can break it down into a nice neat package and stuff it in the pack. The barrels are 243 with an 85 gr Speer bullet and 30-06 with a 220 gr Nosler bullet. Both are great 150 yd stoppers.
The NEF break actions are a bit on the heavy side but, very accurate.

Neck sizing is good for a single shot.

Boy do I hate the first rifle deal. Not being a big fan of the 243, I wouldn't do that. Your going to reload so you can fix up about anything you want to let her shoot. Try your 308 with a 130 gr bullet loaded to about 2500 fps, bet it won't bother her.

That said, I think the best advice you got was the 260. You can load with light bullets,100 gr at around 2700 fps for practice. Then 129 gr bullets at about 2600fps for deer. And then later on 140 gr bullet's at about 2700 fps for elk. You'll never get that versitility out of any smaller caliber. You might also concider the 6.5x55. I just looked at a Howa for about $350 with a cheap scope but also useable rings. I had one, 6.5x55, built for my ex-wife and she loved it. She was about 5'4" and 115#. She likedit better than her 6mm Rem.