I bought the exact rifle for my son years ago....Remington 257 Roberts Mountain Rifle edition.....great gun for a youngster or anyone looking to just hunt deer or antelope.
Our particulat rifle likes the factory Hornady ammo......117 grain bullet. I am sure that there are factory ammo with better bullets out there, but the Hornady ammo works fine for deer. I know that a lot of folks have a favorite premium bullets (Nosler, Acubond, Barnes, etc) and I am sure they will all work just fine. See the attached link.http://www.midwayusa.com/find?dimensionids=9828
From what I have read, your gun will probably like bullets with weights of between 100 - 120 grains.
I think you will like the gun