Suggest going with the barrel that fits your budget. If that's the factory offering, you can always get a local smith to D&T a couple more holes for a 6 screw steel base, probably for no more than a sawbuck or two. You'd save hundreds on the barrel over custom (and cheaper than buying a TC CS just for the 6 screw base at least). I'd go 3 rings when mounting a scope, and the scope is another choice that you have to make. Few of them will stand up to the 375, at least for very long.
If you do go the SSK barrels, I can highly recommend them after having owned a bunch of them (still do). JD makes a very fine product and gets most of my business when it comes to the bigger thumpers. But I'd ventue to guess the factory barrels will shoot well enough to fill the average hunting needs of anyone who's on a budget and doesn't really need to go custom. Wanting custom is another thing. But pride of ownership in something "custom" to show off to your pards comes at a steep price.
My first SSK 375JDJ was a 14" chrome moly with no brake, had just a Weaver base (6 screw) and 3 rings, old discontinued Tasco Pro Class 30mm 1.5-4X. I only shot full load 270 and 300 gr. pills in it, lots of them, and the mounts and scope took it just fine. Current tab for a bare barrel like this from SSK is about $350 (in line with a TC CS, and a match grade Shilen barrel to boot?).
I worked my may up over the years, so #4 375JDJ is a top drawer SSK stainless with full length vent rib, magnaported and currently carries a "starting" price of just under $600 just for the barrel new from JD. Warne steel rings and another Tasco Pro Class 30mm 6X, both in stainless, stainless frame and Pachy's make up the rest of this neat toy (and I am lucky enough to have matching barrels in 257, 6.5 and 309 JDJ's to go with it). No critters anywhere that I couldn't hunt when I take this case along. :wink:
Anyway, just go with what works for you and start enjoying your 375. They are lots of fun to plink and hunt with for sure.
HTH,
L.