I like Jim's answer with one exception. Win 748 which was, I believe, developed for the 308Win. Out of all the powders mentioned, which are excellent choices the Rodney Dangerfield of powders, W748 was again left out of the race as a contender.
I like W748 a lot. Especially in 308win based cartridge cases and those of similar capacity.
My reasoning goes like this.
1.This powder doesn't like to be compressed for consistent performance from shot to shot. It works compressed but in the 7-08 case with the 140 grain bullets there is no need to.
My Remington Model 7 has been rebarreled with a 23.5 inch tube. My load of W748 over CCI 250 magnum primers gives me an honest average of 2940 fps with 140grn Hornady IL BT. bullets. The lowest velocity was 2925 and the highest was 2945. The 2925 velocity was unique as most of the shots were over 2935. These velocities were taken with my magnetospeed last fall. (Makes me wonder why I built the 7x57)
2. This powder is incredibly consistent when it burns. This makes for some very tight groups at all ranges once you find the load your rifle likes. Mine likes a load that is very close to maximum and my velocities aren't achievable in a shorter barrel. I first started using W748 when I was shooting Hunter Bench Rest. From my records, that was 1996. My cartridge of choice was the 308Win.
3. It's readily available and burns consistently from lot to lot and it isn't temperature sensitive to a debilitating degree. I have used it in temps from -40C to +30C and even though there was a definite drop in POI at the colder end the top end didn't change at all. I usually develop my loads in the Spring at temps around +10C.
Like I said, the powders mentioned will do anything you likely need to do. It's to bad you don't mention what you have on hand.
Powder is often the least of the worries encountered by hand loaders unless they run out. The fantastic range of powders being offered today is staggering. The thing you need to worry about the most is to find the sweet spot with pressures and velocities your barrel likes. Harmonics is a very misunderstood and very overlooked condition.
KT, I won't go against what you say but I don't know how you derived your information or on how many or the type of rifles. I have had several 7-08s over the years. I had one as a Wildcat before it became an industry standard. It's a great cartridge. I will agree the velocity range you typed is definitely right in the ball park with 20-22 in tubes, depending on the twist rate. The worst shooting 7-08 I shot was a custom BR rifle with a 30in x 1 1/4in tube. It just wouldn't shoot. It didn't matter which powder, primer, brass, bullet weight or shape I used. Consistent 2 inch groups at 100m and they got worse further out. Velocities were just over 3000fps.
I took that barrel off and stuck it in the bad barrel box.
About 5 years later I wanted to put together a 280 Rem and my cheap bones started to rattle. I started over on that barrel. I cut off all of the chamber area other than the neck throat area and set it up for finishing somewhere around 26in. Turned the tube to a nice length modified medium Palma Contour, cut the threads, then chambered it and twisted it onto a Model 70Win action. That darn barrel shot every bit as well as any match barrel I have owned. Velocities were well over 3000fps. As I mentioned, harmonics change from barrel to barrel for a multitude of reasons. Find the balance and you get an accurate rifle. I believe you found what may be a general sweet spot for a new to the cartridge to start from. That takes a lot of time an work.