The 7mm Rem Mag is an excellent big game cartridge and should serve you well.
I can't say I am surprised by the amount of light bullet advocates here. The 7mm Rem Mag has a reputation as a fast, flat cartridge, and some people like to take advantage of that by sticking to the lighter, faster loads. However, I don't agree with this choice and believe the heavier rounds have several advantages that deserve your consideration.
If I was going to go with a 130 to 150 gr bullet, I wouldn't have even considered the 7mm Rem Mag and would have just stuck with the .270 Win. I tend to prefer heavy for caliber bullets in most things, and one of the deciding factors in me picking the 7mm Rem Mag was the ability to find those streamlined 160+ gr projectiles. There are two primary reasons for this. First, if your hunting is anything like my hunting in Western MT, the terrain might provide you the occasional opprotunity to shoot out past 300 yards, but the vast majority of your shots on game are still going to come inside half that distance, sometimes considerably more so. At these ranges, lighter expanding projectiles tend to be more explosive in nature. Because of this, they tend to destroy more meat, and there is more of an associated risk of the bullet coming apart and failing to penetrate adequately. I am of the persuasion that exit holes are a good thing, esp since I hunt elk with the same rifle and load that I hunt deer with, and any load that can't consistently exit the body of a deer from any angle at any range isn't much of an elk load. The 160 gr loads may not have the screaming muzzle velocities that manufactures like to brag about, but as a result, they tend to have more consistent and reliable performance at closer ranges, with less of a risk of coming completely apart and failing to penetrate. And they tend to damage less meat, in my experience. And while you may be able to find lighter premium bullets that will hold together without fragmenting, these bullets tend to be much more expensive. Going with a heavier bullet at a slightly slower velocity allows you to fill your freezer without emptying your wallet as much, because you don't have to splurge on a super premium projectile to get reliable game killing performance at a variety of ranges.
And when the opprotunity for a longer shot presents itself, assuming the shooter is up to the task, the heavier for caliber bullets again have more to offer. Given two bullets of the same caliber and construction, generally the heavier projectile will be longer, and because of this, will tend to have a higher BC. For example, Hornady lists the BC of the 139 gr .284 caliber SST as .486. The 162 gr SST in the same caliber is given a BC of .550. This is of little consequence at normal ranges, however, it becomes increasingly important as you get downrange. Here's the provided exterior ballistics data for two relevant 7mm Rem Mag factory loads from Hornady's Superformance line (load (muzzle vel in fps/muzzle energy in foot pounds) (500 yard vel/energy) 500 yard drop with 200 yard zero:
139 gr SST Hornady Superformance (3240/3239) (2293/1622) -32"
162 gr SST Hornady Superformance (3030/2933) (2219/1772) -35.7"
While a lot is made of trajectory, I don't think a few inches in trajectory matter all that much. Esp with effective and reliable rangefinders and bullet drop compensators becoming more available, a few inches either way is of little consequence in the field. You have to get out and practice with your load to learn its trajectory anyways.
You should notice that while the 139 gr load starts with a 200+ fps advantage in velocity, this initial advantage has dropped to well under 100 fps by the time it reaches 500 yards downrange. That is the superior BC of the heavier projectile at work. Note that while the lighter load has an initial advantage in energy as well, the heavier load has actually overtaken it by over 100 foot pounds at 500 yards. The higher BC of the heavier projectile also gives it slightly less wind drift (about an inch less @ 500 yards with a 10 mph full value crosswind, according to my exterior ballistics software).
So long story short, I think either of the Hornady 162 gr SST loads should be about ideal. Compared to the lighter loads, this load can be expected to provide more consistent performance with less meat damage and better penetration at close ranges and more energy and "thump" downrange on longer shots.