Good morning and welcome!
My deer rifle of choice is also the 7mm-08. It's "practically perfect in almost every way." My particular stick is a Ruger American, full size. Inexpensive, utilitarian, very light weight and straight forward.
The first ammo I tried was the Hornady 139 grain SSTs. I really wanted them to work, because I have a 280 Rem that shoots them perfectly. But they were 2 MOA at best out of the 7mm-08. So I stepped over to the Federal Premium with the Nosler Ballistic Tips, and I had slightly better but pretty much the same to results. So, hoping vainly that the 3rd time would be the charm, I tried the Federal Fusion with which I've had great success in other rifles. No dice!
So, on the brink of despair, I took a friends advice and tried Winchester Ballistic Silvertips. They are spot on! the first group I tested was 4 shots, 3 of which touched and one was about 0.070" apart from the others. I killed 3 deer with them last year. And of the three, they took a combined total of 1 step. Indeed, I've now begun hand loading and looking for something in that speed range (2750 at the muzzle) with a better bonded bullet to minimize meat loss. (The Win Ballistic Silvertips is the Combined Technologies Nosler Ballistic Tip with the black oxide coating and grey tip rather than the caliber specific colored tips from the standard Nosler line. Nosler Ballistic tips are known for superb accuracy and asinine fragmentation for a hunting bullet...)
But the first three attempts made me a little worried and a little curious. So I started paying attention to velocities and decided that the faster it was, 2800 and faster at the muzzle, the more scattered it was.
But your rifle will be different, so all of this is to say, try a broad range of options, because I think when you find the right one, the 7mm-08 is wonderfully balanced hunting rifle with a lot of underrated capabilities. For comfort of carry and pleasure to shoot, I prefer it over the slightly more capable 280 Rem.
I like to joke that if Jack O'Connor had put his hands on a 7mm-08, no one would have ever heard of the 270 Win.
Good luck and happy shooting!