I would suggest a .243 as long as you don't intend to shoot anything larger than deer with it. It should work fine on deer, hogs and anything smaller. It has very little recoil and shoots flat and is accurate in most guns.

.270 is not a bad choice either, but probably recoils simular to a 30-06 depending on the rifle. Some rifles handle recoil well, others don't. I am pretty small and don't have a problem shooting the -06 if it's in the right rifle with a good recoil pad. No worse that shooting my 12 ga slug gun or Inline ML.

If you are worried about recoil though I would look at the .243, 6mm or a 25-06. All should work for what you want and the recoil will be mild. Great rifles for women and kids. If I get a centerfire in the near future it will be a .243.

Paul