I have both a M96 and a M38. I got them when they first started coming in the country in volume, back in the late 80s. I think both were from Century Arms for less than or around $100. The asking price for decent ones has gone up quite a bit! The old military rifles are well made, most of them in very good condition, it is an easy cartridge to load and they all are great shooters. Get a higher front sight blade though, because they are designed to shoot at 300m.
Also, don't forget the Ljungman AG-42 semi-automatics that came in about the same time. They will beat up your brass, and have a long, heavy action, but are really cool rifles of unusual operation and design.
A local gunshop recently took in a Norwegian 1898 Krag in the original 6.5x55 chambering that is in remarkably good condition. Although priced high, I have been sorely tempted to expend funds on that one.
Winchester and Ruger have both chambered rifles in 6.5 x 55. I have a Ruger M77 in that chambering. It is a great shooting rifle. In fact, I only shoot handloads in it and haven't found anything yet that wants to shoot groups much bigger than 1" at 100 yds. You can also improve on the performance of the cartridge since in a modern rifle handloads in the 50+kpsi range will really make them step out! My favorite load is a Hornady 129 at about 3000fps with Re-19 (don't do this in older military rifles). Ruger also produced a Number 1 in 6.5, last year I think, for one of their distributors as a special.
Winchester also made a production Featherweight Model 70 in 6.5 Swede with a push-feed action in the 90s. One of my friends had one, and in a moment of insanity decided to sell it before he told me he was going to do so! They were planning to offer a Model 70 Classic (controlled round feed) in SS with a Featherweight walnut stock the year they decided to close New Haven. I have the catalog with them in it. I don't know if they actually shipped any, but I was sure planning to get one. That would have been "the perfect rifle".
e/t/a -- apparently they did ship some, because I found a few that had been offered for sale. Here is the Win catalog info:
http://www.winchesterguns.com/products/catalog/historic-detail.asp?family=001C&offset=12&mid=535966