yount - thank you for your service and hope you come home safe...and soon.
Since you have budget issues, why buy three rifles when two will do?
Both Savage and Remington are great platforms from which to begin. My caliber suggestions would be .223 and .308. For all you're asking a rifle to do, the .308 would do it all.
But if you're bound and determined to have a couple of rifles, the Remington 700 SPS Varmint comes in both .223 and .308 (.17 too). You could get one of each and essentially build them as twins. That way when you switch from one rifle to the other, they would feel the same to you.
Remington Model 700™ SPS™ Varmint Specifications
My 308 was built from this platform: My 308 1k Rifle - The Evolution Continues!