What you want is a M1907 style leather sling!
This is what they still use at Camp Perry for competition and what the Honor Guards use on there parade rifles. These slings look great and are great for use when shooting. Here are some of the sling makers starting from the best:
1) Les Tam. The master, the legend himself, usually a few months wait, is suppose to be retired, the best. Nice thick high quality leather, the best:
http://www.lestam.com/products.htm
2) Ron Brown Slings. Trained by Les Tam, just as good:
http://servicerifleslings.com/
3) Turner is the best non-custom or commercial sling, better then the USGI ones. I little on the thin side if you ask me, no brass frogs.
http://turnersling.com/
4) MRT leather sling (M1907). You can still find the USGI ones on eBay and stuff like that for like $15-30. The leather on these slings are thinner then the Turner slings and need a good break in before use. No brass frogs available.
I hope this helps!
Edit: BTW there are a lot of junkie copies out there that won't work or will crap out real fast! This is one of the most copied sling patterns. If you stick with the above, especially 1-3, your good to go!