This is my Remington 700 stainless that I recieved back in 94 brand new from my father I was 12 at the time.
It's a Remington 700 SS 25-06.

I'd like to upgrade the stock on it to help with the accuracy.

What is the barrel profile of this gun?

Is this gun considered a SPS, Varmint, or sendero?

What are some good light weight hunting stocks for this rifle?

I wouldn't be against a nice wooden stock either.

Manners EH1

Browns Precision  Hunter Bench or McMillan hunters Edge are nice too.

I'll second the Manners. Worth the $ and the wait.

How is the accuracy now?  Have you set a baseline with really good ammo of match quality? If there are accuracy problems, it may not be the stock, or even if so, perhaps simple things like action screw torque or minor bedding work might completely solve your accuracy concerns.

.25-'06 is a great, flat shooting hunting round.  It can be made very accurate with handloads and patience, but was never thought of as a target or match cartridge.

If you do need a stock, the McMillan Mountain Rifle stock is on sale right now for approximately $300.  Heck of a bargain.  Long action version is 2.0 pounds, if I recall.  The McMillan Hunter would also be a good choice.  Same weight, slightly different shape.  Both. would work with your sporter profile barrel.

also a price range your wanting to spend.

for contour look here and break out the measuring sticks.

http://www.douglasbarrels.net/contours/

with a 24 inch looks like a remington sporter 03