I was recently in much the same place you are... I played 4th edition heavily back in the day, but I'm just getting into 6th and ramping up for a new Champs campaign, and I've spent a lot of money on PDFs, some of which I feel would have been better as later purchases.
"Champions Complete" seems a good starting point... but be sure you get that an not just "Champions". The latter is a campaign sourcebook that spends hundreds of pages on what it means to run a superhero game (the spirit of my hero Aaron Allston lives on), but is not a rulebook. If you want campaign setting information, that's "Champions Universe," though I think villain books would serve you better in the beginning than the world book overview in the beginning.
I have 6E1 and 6E2, Champions Complete *and* Hero System Basic (don't ask)... Champions Complete would be my starting point if I bought just one book, especially if I wanted paper. If you're going to get 6E1/6E2, then Champions Complete is kind of redundant. I only got it to have physical book to pass around the table (because I have 6E1/6E2 in PDF, which is my preferred format.)
From there, the Villains books are pretty core, but that kind of depends on where you want to go... as you note, the 5th edition books are still very compatible. Point costs change, but the basic rules at the table really haven't, and there's a wealth of information in the 5th edition library that hasn't been reproduced for 6th. I just finished reading the VIPER book and it was great.