That's a good number!
I think it was the 244 Remington early on but they had some complaints of accuracy problems with the popular use bullet weight. Rem changed the rifling pitch, extended the throat and all was well and they renamed it the 6mm Rem to note the change. Case is the same though. '06 case head.

Remington originally put the caliber up in a 'short action' rifle (model 721?). That made the longer and heavier bullets in that caliber unavailable to the users. IIRC they cut the throat extremely short too even for the light weight bullets.
The '03 is a long action and you can take full advantage of the cartridge.
Sometimes custom builders 'blocked' the magazine to shorten it's length when using cartridges shorter than the 30-06 it was designed for.
It can usually can be returned to it's original full length with little work. If the follower has been shortened, milsurp '03 followers (& springs)are still available and a quick fix for that 1/2 of the problem.

A Remington 1903 is a good action too. A WW2 mfg'd rifle so no worrys about the hi#/lo# thing. Some purist in the custom rifle world think they don't deserve a look for a sporter but they're great as far as every one else is concerned. I think the rear tang is a slight shape difference from the WW1 '03, but most everything else is the same. Some say tolerances are looser than the earlier production but certainly no more than 03A3s.

At $225,,you just about stole it IMHO..