Your rifle was built for the 6.5x50 Arisaka, a CIP 38,000 cup / 43,000 psi cartridge. That’s low. Real low, and I’m sure for good reason. I would advise taking it easy with this one. Follow proper reloading practices, work up loads slowly, look for pressure signs, and back off the moment they appear.
Plugging the 6.5-250 into my modified Powley Computer it shows with 140 grain bullets you ideal powder speed is in the range of RL-17 and H414. Using either of those powders, a 140 grain bullet, and a COAL of 2.520", 27 grains would be a mild starting load. Velocity from a 24" barrel is estimated to be about 2,100 fps.
With a 120 grain bullet the ideal powder speed tilts to faster powders in the range of Varget and N540. Using either of those powders, a 120 grain bullet, and a COAL of 2.520", 29 grains would be a mild starting load. Velocity from a 24" barrel is estimated to be about 2,300 fps.
Before you load the first cartridge, if I were you, I’d get some Cerrosafe and do a chamber cast. This would eliminate any questions about chamber dimensions and condition, freebore length, and what is the proper donor brass to use. You could easily do this yourself. Where to get it:
http://www.brownells.com/.aspx/pid=384/Product/CERROSAFE_reg__CHAMBER_CASTING_ALLOY
How to use Cerrosafe:
http://www.brownells.com/.aspx/lid=...fe_sup____sup____The_Gunsmith_s_Secret_Weapon