Definitely 3-cross! There’s no reason for other patterns, as far as I know, unless you are obsessed with aesthetics. Once I even asked master wheelbuilder Josh (formerly at UDC, now virtually at UDC) about this, and he told me that double-walled rims had made 4-cross unnecessary -“overkill,” I think he said.
Anyway, I have twice rebuilt my 20" wheel. The first time led to a spoke breaking every few weeks, but the second time was a smashing success, even though I had damaged a few rim eyelets with some of my earlier fiddling around. My wheel ended up stronger than before, I think, and hasn’t even needed truing in months, despite the fact that many bike shop mechanics had told me I should just buy a new one.
This doctor-said-I’d-never-walk-again story is largely the result of a tutorial and other advice posted here and other places by jtrops. He said his tutorial wasn’t meant to be comprehensive, but it is extremely helpful, and if you follow the links I posted in the discussion of it, you more or less end up with the full picture, at least as I understand it now. There may be some things to keep in mind when rebuilding a 36 instead of a 20, but I’ll let someone else fill you in on that.