Start by picking your parts. You may love an a5 but hate a chassis or vice versa. You may drool over a 30" Broughton or may be like me and be just fine with anything in stock.you may want a dbm.....you can see where this goes. Labor is covered by Landon a few posts back.
I'd either screw a tube onto what you have, or save my scheckles and build it once. If you don't have a 12 pound rifle yet.....I'd try one before you buy one. ....just me.
high country, makes a very valid point. Sometimes, certain things may sound like a great idea and we "think" it's what we want but then we get it and quickly realize reality is vastly different. I think this often happens when people select an aftermarket stock for their build. Probably why you see so many slightly used aftermarket stocks for sale. I know, I've, made this mistake before. On my very first full custom build, I just knew I wanted a MCM A5 stock. I'd never even held one in my hands, let alone shot anything with one on it, but, I knew that's what I wanted. The gunsmith that was doing the build asked me multiple times before he ordered it, if I was sure an A5 was what I wanted on this particular build and the notion in my head always lead me to say yes. Then I got it and quickly realized maybe an A5 wasn't the best choice for this particular build. Make no mistake, an A5 is a fabulous piece and I still have two of them on different rifles but I think they are more of a purpose built stock and depending on how or what you plan on using the rifle for, they may not always be the best choice.
Stock selection is just one of the things you'll want to really do your research on. Barrel length, muzzle brake, trigger, the type/style of bottom metal, if any, you want and don't forget about the finish. Do you only want it bead blasted or do you want some type of coating, like Cerakote, put on it. Finish type is personal choice but having had rifles both ways, I highly recommend Cerakote. A good Cerakote job, in my personal opinion, is worth every penny!
Pricing out a full custom rifle will be something like this. Prices for labor/machine work will vary from smith to smith but this will be pretty close. I'm going to price this out for you with a Stiller action. Stiller is a very good custom action and they are the least expensive of any custom action that I'm aware of.
Stiller action $950-$1000 If you decide to stay with your Rem 700 action instead of using a custom, you'll spend $225-$250 to have it blue printed/trued/accurized different smiths call it different things. If you find someone that does it for a lot less, great, just make sure they are doing a full blue print and not just truing the face and lapping the lugs.
Barrel fluted $450-$500 (-$125 non fluted) FWIW last fall I ordered a Benchmark fluted barrel for a friend it was $430 delivered to his gunsmith)
Trigger $135 Timney, $235 Jewell, Rework Rem. factory trigger $50-$75
Muzzle Brake $200-$250 installed. Price will vary depending on size and whose you use. I'd recommend a baffle type not a radial type.
Barrel work $200-$250
This will give you an idea of what is all included in that price, I don't know that all do this but this is how a friend of mine (Kevin Cram) in PA. that is an excellent gunsmith does it. All barrel work is bore indicated true within .0002” or less of concentricity using PTG live pilot indicating rods and Mitutoyo .0001” dual indicators. in MCR’s barrel fixture. All chambers are cut using PTG live pilot reamers held in a JGS floating reamer holder. Single point turn and thread to a class 3A fit. Chamber to minimum head space. Single point crown. Custom engrave cartridge designation.
Stock $225-to as much as you want to spend. Depending on what you want, you can pick up a nice HS Precision take off stock from a Rem Sendero, Rem 5R, Rem LTR, Rem 700P, Rem PSS in the $225-$250 range. Or, you can go with a MCM or Manners, both are VERY good, from around $350 for a used one on up to as much as you want to spend. If wood is your thing, you can spend as little or as much as you want there, too.
Bedding and Pillars $75-$250 Stocks, like HS Prec. or B&C, that have full Aluminum bedding blocks integrated into the stock, can usually get by with skim bedding and that'll be on the cheap end of the range. Fiberglass, wood, and pretty much any stock without the aluminum bedding block in them will cost more to bed and on a big thumper like a 338 RUM, I'd always have pillars installed but I'm sure you can find those that think differently, too.
Bottom Metal $25-$500 This is another area with a huge price range. If you go single shot the only cost you'll have is trigger guard. Standard BDL type setup $150ish range. The last Detachable Mag system I used on a build was a Seekins and with one 3 round mag it was $450 installed. That was two years ago. DM systems look very cool and most work fine but they have their quirks, too. Depending on the brand and how many rounds the mag holds, they can stick out the bottom a far bit. Some feed better than others and again, depending on the brand, vary in allowable overall length of the cartridge. HS Prec. makes a very nice compact setup that you barely know it's there, but, they have a shorter allowable O.A.L. compared to say the Seekins DM system, which allows for a longer OAL but is more expensive and doesn't feed as smoothly as the HS Prec. And don't ever lose on of those mags because they are expensive and you'll be relegated to single feeding if you do.
Finish $0-$250 You can go with no finish or just a bead blast finish and depending on your gunsmith it'll cost little to nothing. Or, you can go with something like a Cerakote finish and even though it'll cost you a couple hundred bucks, my personal opinion is it's, easily, worth the money but you may think differently.
I think that about covers it. If I left something out, I'm sure someone will mention it.