Action?

What action did they use for the STW?

STW is an abreviation for (Shooting Times Westerner).
Originally created as a wildcat cartridge by necking down a standard 8mm magnum case to 7mm.
It is essentially a ballistic clone to the 7x300 Weatherby, which is an older wildcat and uses the 300 WBY case necked to 7mm.
For a period of time it became a factory offering by at least one gun company.
Id say the Rem 721/700 actions were the choice for the early guns, although any good action including the Savage 110 can be used.
The Rem 7mm ultramag has slightly higher velocity potential than both of the others mentioned.

Been a long time since I've had my hands on a standard long-action (30-06 length) Savage, but I know the OAL for the 7 STW is slightly longer (3.360" for the '06 v. 3.600" for the STW). The .375 H&H and Remington Ultra-Mag's share the same 3.600" OAL as the STW. Inside measurement of an '06 centerfeed mag I happen to have here is just a hair over 3.500" so the magazine port on the bottom of any standard long-action (30-06, .300 WM, etc) will likely be too short.

That in mind, you would need to find an older staggered feed 110 action that was originally started out as a .375H&H or RUM which aren't all that common, and the accompanying magazine box. I know Charleslv had a new in box Savage rifle in a RUM cartridge listed for sale in the classifieds not to long ago. Don't know if it sold or not, so you might send him a PM to see if he still has it.

And to add to what Mr. Mcfurious said, that all can vary depending on the bullets you choose to use.
The longer/heavier ones could spell doom for even the longer actions as for using the magazine.
Which is exactly why many guys don't use a magazine and just single feed the gun.
The deeper you seat the bullet in order to fit the magazine, also means less powder capacity in the case.