[Wyosmith]

Sticking my nose back in again:

It seems the key points are there---------
#1 The rifle has to be good for a small woman. So it can't kick much and I'd assume it can't be too heavy
#2 It has to be a proven performer on White Tail Deer.

So the counter questions are these:

(A) Are you dedicated to a bolt action?
(B) Will the rifle ever be used for anything larger then deer?

If it will never be used for anything bigger that deer you might look hard at an AR15 in 6.5 Grendel or 6.8 SPC. The AR15 kicks less than any other rifle I know of for the power it generated with the 2 cartridges I mentioned.

The 6.5 Gren. is about like a 6.5 Jap in power but shoots a bit lighter bullet.

The 6.8 SPC is about like the original 257 Roberts in power shooting a 115 grain bullet instead of a 117 grain bullet like the Roberts, but shooting it about 100 FPS faster if the barrel length is the same.

Another gun to look at is the Browning BLR in 260 Remington or 243 Winchester. In the light weight version it's truly a delight to carry and quite accurate in most examples

If the budget allows but if you can't go over 500 you are far more limited.
At $500 and less your choices are much skinnier. One to perhaps look at (if you reload your own ammo) is a Savage Axis with a fast twist barrel in 223. Shoot only Bonded, Partition bullets and/or expanding solids for deer.

And there are a few places in the USA today you can buy an AR with a 1-9 twist for about $500