I think your leaning towards the 7mm Rem Mag is a FINE choice.
The .338 class of cartridges are very fine as well.
And this brings us to rifle choices.
Many of us get a "new cartridge" itch every now and then.
Allow me to introduce you to a new idea (if you have not heard of this:
Barrel switching.
And the traditional rifle ....... has until a couple of years ago was the SAVAGE bolt actions (some Stevens models too)
But lets also mention the Remington 700 ..... it's in play as well.
Go to this web site:
http://savageshooters.com/SavageForum/
Not only is everything "Savage" found there ....... but with one of the Vendors and McGowen barrels ...... the term and concept of Rem-age barrels was born.
What is Rem-age? ....... it's custom barrels made for Remington 700's but with a custom nut that are installed with a barrel nut wrench made for Savages.
So in one broad brush swipe one can either have a Savage barrel switcher or a Remington 700 .......
With the Savage one can change bolt heads and not only change chamberings but go from one class of cartridges to another.
With a Remington 700, one is going to have to change bolts to switch cartridge families ..... but that can be done as well. If you own a magnum face bolt ..... you can switch barrels without a different bolt so long as the case head of the cartridge you change to is the same.
Headspacing under this system is best accomplished by using a Go-gauge ...... many use a FL sized casing ... but it is undeniably springy ..... to each their own.
I could go on and on ..... but I would strongly encourage you to register over at Savage shooters and learn more about these systems .... and even pay the $12 for one year's worth of paid membership ...... and get into the classifieds so you can see the "whole world" open up ....
And as to chosing rifles ......... on a budget ..... I would suggest a new or used Savage or Stevens OR ..... a good used Remington 700 .......
The Remys are the gold standard, the triggers are EXCELLENT .... if you go with one and care to help the trigger .... send me a personal message here or over at Savage shooters and I'll gladly send my instruction set I found on the internet ..... which led me to tune my own ......... my 700 is positively stunning now .......
And don't get me wrong .... the Savages can be set up pretty good too ...... there are some more twists and turns but more flexibility .......
Whatever you decide ..... Enjoy!
Three 44s