The Browning would be a fantastic rifle for you. My buddy had a Browning Hunter (wood stocked 300wsm) that shot really good. He end up trading it for a Tikka. Only reason he traded was he won the Browning, and wanted a gun with a synthetic stock, and thats all the local gunshop had in 300wsm at the time.

My brothers fiance (5'2" 100lbs from California), actually has no problem what-so-ever shooting my 7mm Rem Mag Browning. I'd call the recoil on it almost non-existent, it does have muzzle flip, but thats about it.