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7mm WSM or 7mm SAUM

SAUM. depending on what bullets your gona run. SAUM has a little shorter case so your not over stuffing bullets in an AI type mag. Tikkas dont have a ton of room when used as a long action. If your running the factory plastic mag you could go either way and be ok
 
Both brass are unicorns. Before you build a rifle, stock up enough brass to toast the barrel.

Basically, if you want a short action, go SAUM. If you want a long action, WSM. The mag length restriction of a short action neuters the WSM. The SAUM was really designed to maximize what can be done in a short action. The WSM can work in a short action, but not with the long, high BC bullets set to ideal length.
 
Brass is tough, but can be found. I found some norma brass recently amd have been slowly stocking up on nosler stuff as well. It can be found but it's expensive.