You did good there. The Tula '40 is pre-barbarossa and should have a higher quality of machining than most. For the Mosin, here's the rundown:
Remove from the stock and check the wood at the contact points with the receiver. Sometimes its so deeply pithy it doesn't make a solid base and you'd be advised to pick up a replacement sporter stock or put in some metal spacer/washers between the wood and the receiver for a more solid fit. The spacers can also be used if you find the stock is pressing too much against the barrel. AN old Finnish trick is to put specially shaped washers between the stock and the receiver to lift the barrel up off the wood out front.
Make sure when putting the stock back together to tighten the receiver screws well. A lot of inaccurate Mosins are caused by loose screws.
Check the crown for any serious damage. If the lands are crisp at the end of the bore you should have a good shooter
To maximize accuracy, slug your bore at some point. There's a lot of variability in Mosin bores. Yours should be about .311" but it may have been re-reamed at some point later in the war to freshen up the rifling.
There's a wide mix of 7.62x54R ammo available from funky old surplus ball to modern Russian production and high-end Norma and Lapua match loads. Most Ruskie 91/30's tend to prefer the big 200 grain modern production stuff from Wolf or Barnaul or the old heavy ball loads. But each Mosin is a little different so experiment around to see what it likes.
To clean the bore, I highly recommend the M-Pro cleaner and bore gel. You don't need to use very much. Just coat the bore and let it sit, then scrub per directions.
On the K-31, you should find it's still in excellent shape. Most of them, even those with badly abused stocks, are nearly mint inside. The Swiss were among the first to switch to non-corrosive primers and they took very good care of their rifles.
You will find it shoots best with standard GP-11 ball, which is fantastic but somewhat expensive surplus ammunition. Don't be surprised if you find yourself getting MOA groups with it. The Portuguese stuff isn't as good, but Hornady is now loading its own 7.5 and the supply chain for this stuff and the new production brass seems to slowly be catching up with demand. It uses standard .308" bullets and you'll proably find it likes weights from 160 to 180 rather than very heavy or very light bullets.
Check under the buttplate for a special surprise
