Assume you want the LR or Varmint version of that Sako A7, which is similar the the 700 and Savages you are asking for. The normal A7 is not set up as LR friendly OTB.
For someone trying to go LR on the cheap, this isn't a bad way, but as I've done the same using a Sako 75 & Browning A-bolt, both in 7RM, I must say while it can be done, both of mine shoot sub MOA to 800, it's hard to get the velocity you want, hard to get the real high BC bullets like 175/180 .284's to shoot well or even fit using factory guns, and they tend to be verd dependant on precise reloading formula/technique. Man was that a run on sentence.
You might find that instead of trying to save $$ with this tact now, and spend an extra $500+ burning out a barrel fine tuning, maybe go semi-custom. Rem or Savage action, $200 B&C medalist stock bedded, and pick up a good $400 barrel and get it properly chambered by a good smith who is likely to give you a starting load that will shoot sub moa day one.
Now, if you really like doing load development, then by all means.
PS I think and A7 in the config you want could be had brand new from Cabela's when they have a sale pretty close to that $1k mark.