As far as I know, the 700 action is the same across all models, except for short, long or magnum length. I haven't been involved in LR shooting for several years (a decade) so I may not be correct, but the models are determined by stock configuration and barrel profile, not any difference in action quality or type.
While you are going to indeed want to drop it into a dedicated chassis, wait on it. If you're really just getting into the game, you'll gain more accuracy through practice and handloading than you'll be able to get by shooting factory ammo through a customized rifle. Find a load the rifle likes and it will likely be a year or more, depending on your practice regimen, before you'll benefit from any money spent to upgrade the rifle itself.
Your Kimber rifle will do just fine. You don't need an identical scope on it, in fact it doesn't have to be scoped at all. Rimfire is where it's at for refining technique and form at far less cost than your centerfire. Dryfire is very important, too. Between dryfire, rimfire and centerfire, probably 20% of your shooting will be sending .30 caliber bullets downrange. As your form becomes more refined and ingrained into muscle memory, rimfire will become a little less important, but never obsolete, and dry firing will become more important.