I'm not a gunsmith but I've shot my share of rifles in various calibers out to some decent yardages and brought my fair share of meat home for the freezer. I've learned to respect any rifle that shoots to it's capacity... Especially when I'm shooting to mine...
A rule of thumb for me, is that it's takes time to learn what any given caliber, load and type of bullet can do. As is often the case, I was looking on the net and believe that Remington is not longer producing the 7mmRUM in a production rifle. It may do so out of their custom shop, but I don't recall seeing anything in their more mainstream production rifles in 7mmRUM. However, there are those who know the underpinnings of various Remington production rifles much more extensively then I do, but I'm just stating this information as something you may want to check out further. Remember that brass for the 7mmRUM will be a bit pricey, as will the amount of powder needed to reload your cartridges.
A baby step down from the 7mmRUM would be a 7mmSAUM which again, seems to be exhibiting some of the signs of the death rattle... At least as a production rifle. Brass isn't impossible to find, but it's not an item that a lot of reloading supply gun shops readily carry. So yo may want to keep that in mind before you make your decission.
Now another 7mm shooter is the 7mm STW. It has a lot of pop and can get the job done at least as effectively as the 7mmSAUM. And is probably right behind the 7mmRUM. Now the 7mm STW was created about 2 decades ago and was based on a necked down case from the Remington 8mmMag. This case is the same demensions as the 7mmRM but it's longer, so you can add more powder to get down range, faster and somewhat flatter then the 7mmRM. If you wanted a gun of the 7mmSTW set-up you can have a gunsmith ream out a 7mmRM so it will fit the demensions of the extra length of the 7mmSTW case.
Some work on the ejector port may need to be smithed too. So that the longer &mmSTW can exit as well as it need be.
Now you have the 7mmWSM and the 7mmRM. Both, and in fact all of the various conversions and diversions of the 7mm bullet can produce some decent numbers. If you want something that has enough authority for most game, and is probably more easy to obtain, then the 7mmRM is probably one of the primary choices. If you like short actions then I would suggest the 7mmWSM. very nice ballistics there, and still available in a production rifle.
Now there are more choices: Like the 7mm08 which is a necked down version of a 308.
You can look at a 7-30 Waters which is a necked down 30-30. this is probably one of the more rarer 7mm cartridges and was usually religated to lever action model 94s. Which, if it was ever built to shoot lever evolution ammo, would do well on deer to respectable yardages beyond what it is capable of doing now.
Also there are at least two more 7mm cartridges in European demensions and you could look at those options as well.
All of these options provide for some interesting reading, thinking, pondering, and if possible, try shooting some of them before you make your final decision... Or, you could have one of each, and see which one wins the race as your all time favorite.