It's tricky to know which series are complete, since I haven't read many to the end (and honestly I suspect a lot of the ongoing series lose steam after a few books, just like TV shows that get run into the ground), but here are a couple of suggestions:
The Euphoria Online series by Phil Tucker, starting with Death March - This is a trapped-in-VR story. It's a complete trilogy of fairly short books, and I enjoyed it.
The Mage Errant series by John Bierce, starting with Into the Labyrinth - This is a straight secondary world progression fantasy, starting with a magic school. No portals or VR, so maybe not what you're looking for. I also had to check whether this was actually complete, since I am reading book 5 of 7 right now, but it does appear that book 7 is the finale. I can't say whether it sticks the landing, but I have enjoyed it so far.
If I think of any more I will add them.
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