Re: weatherby or remington 700
$600 for the rifles you list will be a challenge. You may find one on the used market but it'll be difficult. Remington 700 in 7mm has been around since the 60's and most of the gun shops I visit have one or more on the consignment shelf. Building one for $600 ain't gonna happen. The action will cost nearly that much, perhaps more depending on what you choose.
Both are fine rifles. Suggest you visit gun shops and see how they feel, which action you like best, and take it from there.
I have a great woman, fantastic kids, a warm place to sleep and an accurate rifle. Life is good ..............
Hunter Safety Instructor - Rifle/Pistol Marksmanship Instructor - NRA Life Member
American rifleman's triad - God, guts and guns. It built America and it'll preserve America. Abandon one and you lose them all.