When starting a new campaign, must the Overlord choose to play with either the Basic I deck or the Basic II deck? Or, is the Overlord allowed to customize a deck by included cards from both?

You have to choose, before the campaign, if you are going to use Basic or Basic II. You can not mix them.

Thanks for the info. Do you have a rule I can reference in the future?

New Overlord Deck section of the LoR rulebook, page 4.

You have to choose Basic I or Basic II, you can't mix both.

Basic II is fun to play with, I tried it earlier this week and it have some nice surprise for the Heroes. I really like how some cards are a bit more powerful when played on a specific Archetype.