The most critical thing about a stock is that it fits you.
If you haven't already done so, try to get some time at least holding, if not shooting, a variety of different stocks. Just because something looks cool, doesn't mean that it's going to work out well for you.
A couple of things may be important to you:
comb height - very important to achieving a solid cheek weld
length of pull
thickness of the forearm
angle of the grip
All these things and more contribute to how well your rifle fits you, and feels. From what you've written, I'd say you're looking for a general purpose stock, which will be useful in a variety of different field positions. That sort of thing tends to favor the more general-purpose stocks, rather than the specialized stocks which may be more suitable for prone or bench use only.
BTW - don't discount the value of a stock which is handy in the sitting or kneeling positions. I've taken a fair amount of game from sitting - much more so than from prone. Where I hunt prone generally isn't very useful, too much grass and brush in the way down low.
Long a favorite for general use with a precision rifle is McMillan's M40A1 stock. A somewhat modified version of it, the M40A1-3 was introduced in recent years and is a big favorite of mine. It has a slightly higher comb, and a thicker fore end with a bit of a taper to it. Very nice. Their A3 stock is one of the easiest to use from a variety of positions and is very popular with LE snipers who may have to shoot from standing, sitting/kneeling or prone. Most people find it very comfortable.
One really great thing about McMillan is that you can order the stock your way. Your length of pull. Your choice of fill weight. An adjustable cheekpiece if you want. Regular sling swivels or flush cups. How many and where? Custom colors. Perhaps a fore-end rail if desired. Another great thing about McMillan is that the doggone stocks are tough. Very tough.
Again, it's how the stock fits you that's important. What I like in the fit of a stock may not work at all for you. People are built different. Two of my LR shooting buddies are built completely different, one guy is 6-05 or more and probably close to 300 pounds. Our friend is maybe 5-06. Maybe. They do NOT favor the same stocks...
Where to go to sample some different stocks? I'd highly recommend going to a highpower match where guys are using bolt action match rifles. Their rifles have to be useful in prone, sitting and standing. You'll likely find a lot of different stock configurations there. Also, I've heard from a few people that McMillan will send you a stock to try - if you're really nice to them. A major rifle-builder may have a few different stocks sitting around too. Worth asking.
One thing to remember about the Remington factory stock - is that it is mas produced to feel reasonably good to a lot of different people. I have one, the HS Precision version with the aluminum bedding block. It's okay - but the LOP was too short for me and the comb way too low. Both of those things can be changed, at a cost. I simply replaced that stock with a McMillan and have been happy ever since.
My favorite stock is a walnut stock turned by Jim Cloward and built in the old Dunlap style. I use it for both across-the-course competition and prone matches. Have also used that rifle for some varmint shooting. That stock feels different from anything else I've used, but works really well for me.
Good luck with your project! Regards, Guy