For the amount of frogskins, I think it's gonna be hard to beat a Savage (with Accutrigger) if you want to go "new"...

My best advice is to get the most expensive optic you can possibly afford and slap it on whatever rifle with the remainder of your budget... even if it's a used rifle....

regarding suggested calibers and recoil, I'd need to know more to advise...

if it's strictly for whitetail inside 350-400 yards, it's going to be hard to beat the .243...

if you can really shoot well, the 223 should not be overlooked...

260, 7-08 are also worth consideration...

Myself, I find the 270 is the best combination of ballistics per recoil energy for anything Elk sized and below...

Lastly (and again) GET KILLER OPTICS!!!!!