Firstly, unless you're going to be shooting PEOPLE, it's not a sniper rifle. Second, most of these rifles aren't true sniper weapons, but more designated marksman weapons. They're big, they're powerful, they're quite accurate, but they're not the half-MOA you'll expect from a sniper weapon. 1-2 MOA is more what you'll be looking at.
I'm pretty sure the only semi-auto 8mm is the Zastava M76. As for 7.62x54R, there's a few choices:
Romanian PSL: The cheapest option, available for under $700. Inexpensive, reliable, pretty accurate, lightweight, and has a great muzzle brake. The major downside is the scope that comes with it is bad and really should be replaced. It takes a standard Dragunov-style optics mount, and BP-02 adapters exist that allow you to use any Weaver-based scope. Mine's wearing a Simmons 6-18x50.
SVT-40: The original semi-auto 7.62x54R rifle. These can be had for around $1000. From what I've seen, they're very lightweight (8.5 pounds), reliable, and have a good muzzle brake. They usually have incredibly nice wood for a surplus gun, as they were rearsenaled after World War II and never used again. Just good-looking rifles. This is your lightest-weight option.
Dragunov SVD / TIGR: The real deal, but prohibitively expensive.
Chinese NDM-86: High-quality Chinese clone of the SVD, usually in .308. Also very expensive, though these are probably the best choice for someone seeking a real SVD.
