Barrel contour these days is really about overall finished build weight. With your average competition chassis(before weight kits), an ATACR, G3, Khales 25x or 35x scope, heavy unimount, and M24/ Heavy Palma, muzzle brake, bipod you're looking at about 18 - 20lbs. That's on the lighter side of a PRS comp rifle. 10 years ago it would be considered heavy but today people are running 23 -28lbs. That's why CRB Comp or the Proof Heavy Comp barrels are more common than ever. You can certainly add weight by buying a weight kit, but it's additional money to get there and you can only stack so many weights on most chassis. Weight in the barrel is free weight. No cost difference between an M24, MTU, Comp, Heavy Comp barrel. And you will only be able to add about 4lbs in a lot of the common weight kits. Some more, some less. I would err on the side of a heavier barrel and then fine tune my weight with additional side or forend weights as necessary.
Here's a sample of weight measurements for you.
XLR Envy Pro C6 with PRS weight kit package($460), Comp contour 25" barrel, Hawkins updraft, single pull CkyePod, NF ATACR, Hawkins Heavy Tactical mount, TL3 : 24lbs
Zermatt TL3, ATX chassis with folder, NF 7x35 ATACR, Hawkins Heavy Tactical mount, Hawkins Updraft brake, CkyePod, 26" CRB Comp, 4.5lbs of side and fore end weights($400): 26lbs
Zermatt TL3, ATX chassis w folder, NF 7x35, Hawkins Heavy Tactical mount, 26" Heavy Palma, TBAC U9, CkyePod: 19lbs
ATACR in Hawkins mount: 3.5lbs
Single pull CkyePod: 1.5lbs
AICS mag: 6oz
Hawkins updraft brake: 6.5oz
Envy Pro before weight kits: 4lbs
PRS Comp package: 6.5lbs
Zermatt TL3 action: 32oz
26" M24(0.920 at the muzzle): 6lbs
26" Proof Comp contour (1.000 at the muzzle): 6.5lb
26" CRB Comp contour (1.125 at the muzzle): 7.5lb
Average precision rifle suppressor with cover: 1lb
1.2" straight tube barrels are an option but they can run into fitment issues with certain chassis and shrouds. The CRB Comp or Proof Heavy Comp contour at 1.1" muzzle is kind of the best of both worlds in fitment free and max weight.
As far as cartridge I think you could go either way on 6.5CM or 6CM. I haven't seen barrel life be all that significant between a 6 Creedmoor vs a 6GT. I have seen more variability in barrel life from barrel to barrel more so than cartridge to cartridge. I just had a 6Dasher go out at 1400rds. I would favor 6GT over 6CM for recoil purposes but I think you need to be reloading. I guess there's technically 6GT loaded factory out there but it ain't like the availability and price of CM. Maybe there's an advantage of going 6CM so as you begin accumulating reloading gear and eventually decide to go 6GT you can at least have the efficiency of 6mm bullet commonality. Regardless, when you get to 500-600 rds get your next barrel in the queue.