I own a 7mm. Great gun with bullet weights from 110/120 to 170gr. I have used it for small varmints, but as stated it did dismember a rabbit that I hit at about 150 yards. It is super accurate with the right load length and you will want to reload for it as bullets are a bit expensive off the shelf.
Are you talking about 7mmx57 Mauser or 7mm Rem Mag?
7mm Rem Mag was used by the Secret Service with a 168gr bullet. It was later replaced by the 300 win mag which can fire a heavier bullet but also has more recoil. The 7mm is very flat shooting. You can zero it at 600 yards and it will reach out to 1,000 and more (I think it held the world record at one time).
If you are planning to keep the fur, the 7mm Rem Mag might be too much. If you just want the varmints "gone" it will work fine.
There are several to chose from; 7mm Remington Mag, 7mm Weatherby Mag, 7mm Mauser, 7mm WSM, 7mm Saum, 7mm-08, 7mm STW, 7mm Rem Ultra Mag, 7mm RCM, 7-30 Waters, 7mm TCU, and a few more that I can't think of right now.
They will all kill varmits quite nicely.
If you can afford the ammo, a 50 BMG is a fine varmint rifle too, just wouldnt be much left when ya hit the furry critters. I personally use a .308, and dont feel as though its "too much" for the varmints that we find around these parts (mainly wood chuck and coyote) Nothing says you cant hit prairie dogs with a 7mm, just a but more than what it takes to knock smaller stuff down, and pop their boots off.
7mm Remington seems like a pretty versatile round. I'm certainly no expert, but a friend of mine who's an extremely avid outdoorsman and hunter has used his everywhere from Texas to Africa on things from ground hogs to black bears to zebras. I'd trust his judgement on such things if I were in the market for an "all around shooting critters of various sizes" gun.
If you just want to kill them, it's fine. If you want to keep any fur, look elsewhere.
22-250 is about the nicest varmint round, in my book. I'd even consider .243 a bit overkill for varmints if you're interested in keeping any fur. Only caveat being if you're wanting to shoot prairie dog towns and plan on running a ton of rounds through it. 22-250 will chew up a hot barrel a bit quicker than some other chamberings.
I would think that a 7mm bench rest would be a good choice. The smaller bullets could take the small stuff and the bigger ones could take deer. I would think it would be a great choice for a all around rifle.