No matter which round you go with, if you have a good buddy gunsmith that is REAL reasonably priced (and is a decent 'smith) or will do it for a case of beer, I'd say the best thing is to put together you own rifle. Really all he will need to do is true up the Remmy action and chamber/install (that includes head spacing) the barrel. In MY opinion, a muzzle brake is not really worth spending money on as the only time it does you any real good is when shooting for zero or playing at the range.......but it usually is REALLY GOOD at annoying everyone around you. Not necessary for a HUNTING gun unless you are
EXTREMELY recoil sensitive! When you are out hunting, keep in mind that you have to carry it around 99.9% of the time and only shoot it .1% of the time...and if you hit your target, the animal will never know/hear the difference. Based on personal experience, you will never even feel the recoil!
Also, money spent building a GOOD, ACCURATE personally satisfying rifle is money well spent, so if you DO go a tad over budget go ahead. You will get over it really quick if you spend a tad more than planned and will have a great rifle to shoot FOREVER, but if you scrimp, EVERY TIME YOU PICK THE RIFLE UP you will get all disappointed all over again....FOREVER! Trust me on this...I am an old guy and have lots of guns, but only a VERY FEW of them make me smile every time I even just LOOK at it!!
SO, here we go:
Remmy 700 action off of a donor gun: maybe $150.00 (or maybe even you already have a junker behind the bedroom door...so ZERO dollars)
A good barrel: Minimum about $330.00 (NOT the place to "economize")
Good recoil lug--maybe $50.00
A simple and adjustable Timney trigger: $125.00 (NOT really needed oftentimes, as
some stock triggers CAN be OK with a little work)
A stock that fits you right: $350.00 to maybe $700.00 (or UP

) depending upon your tastes/budget...You want bling or a good, practical stock??
Decent base/rings of your choice about $150.00
If you have an old junker behind the bedroom door and can use the action off of that, just toke your gunsmith buddy the $150.00!! Keep in mind that the donor gun does NOT HAVE to be a magnum action, but it is convenient if it is....If not, the bolt face can be opened up as needed, so it only has to be a long action!!!
HAVE FUN!!