Virginia has an “instant” criminal background check, assuming the system is up and operational. I don’t think I’ve ever had to wait more than about 1/2 hour or so, and that’s on a weekend at a gun show when the system can be pretty busy, or at least the link from the gun show building to whatever system is being used. There is no formal waiting period in VA.
Now, you can’t purchase more than one handgun in a 30 day period unless you apply for a collector permit/waiver, as one might when purchasing a collection or matched set. The quantity of rifles is not limited.
Or if you ae a Virginia CCW holder.