I just picked up a Rem 700 V.S. as a project rifle. I guess the best place to start is with mounts and rings, which ones and why?
Have a nice evening,  Rabon...  

I only use Leupold or Redfield (same thing) one-piece steel. They are very strong and sturdy.

Rabon,

What's your project?

I use Redfield JR 1-pc. base and Redfield low rings on my Remington bolt-actions, including the XP-100R in .223.
I prefer the look of the 1-pc. base under the scope and this style overcomes any misalignment of the scope mount holes better than the two pieces, if there is any.
I believe for my uses these are strong and accurate enough for adjustment.

Secretly, I want to install the "Conetrol Custum" high polish rings and 1-pc. base on a Remington 700; probably a 1994 Classic in 6.5x55 Swedish, when I can arrange to get it someday.  It will go in the Bell&Carlson Thumbhole Sporter stock that my 7mm is in now.  
That will be my "project" rifle as I like the 700; the Swede cartridge; the stock and the mounting system.  Scope for that one will probably be a big NIKON.
A sleek and personal choice.

What's your price limit and where on the quality spectrum are you looking at? If on the high end I'd recommend Badger Ordnance rings and base. Simply nothing to regret with such high quality. The base with additional 20 MOA is great for long range shooting if you plan on doing that sort of thing.

For my Remington 700P LTR, I went the economical route and got Smith Enterprise one piece base (~$60-$75) and A.R.M.S. quick release 30mm rings (Medium height for my Springfield Armory 3rd gen 10x56 Mil-Dot and Low height for my Tasco SS 10x42). No complaints here and the set up seems to hold repeatable zero when interchanging between scopes.

I've got a shooting buddy with a Rem 700 VS who uses Leupold Mk IV one piece base and the very affordable quick release Leupold rings, and his set up works excellent judging by his awesome groups.

Lastly, whichever rings you buy I'd highly suggest lapping your rings. Sinclair international sells an affordable ring lapping kit for less than $20.

Congrats on your new toy and let us know what you decide on and how she prints.

-jsr75