First, CONGRATS! The only downside is that for some folks buying their first Mosin is like eating Lays potato chips. :-)
My *personal* opinion is to go out and shoot it. There are a few real beat-up dogs out there, I got one in a 91/30, but most of the M38/M44 seem to be of the refurbished and stored variety. Tight, and in an overall very good condition.
While checking headspace does not seem to be that difficult, I think if I really wanted to be reassured of the condition of a new to me Mosin purchase, I would take it to my local shop and have the gunsmith give it a full once over to include the headspace check.
Post a pic if you can. I’m starting to feel the wallet rumble. Been awhile since I’ve been to a gun show to check out the Mosins and the SKS :-)
I will likely just buy a “go”/”no-go” gauge and go shoot.