The only type of paper I've never tried is glossy cardstock or photo paper. It explicitly says on the Gelli Plate web-site that it will damage the Gelli Plate so I've not even tried it.
My favorite types of paper to use are the Mixed Media papers below....
L - Dick Blick MM; Center - Canson MM; R - Strathmore MM
These are cardstock/index paper - They both work pretty well but the Georgia Pacific (R) seems to pick up a more even coat than the Neenah Index paper.
L - Crayola Watercolor/Marker paper - Looks & feels like copy paper
R - GP standard copy paper.
This is my other favorite (L). It is printing making paper from Dick Blick. It's a bit larger than regular papers and it's got a great feel wet or dry. The prints stay flexible and can take layer after layer after layer of paint.
The smaller example which took paint really well is Canson watercolor paper. I don't use it often since it's more expensive but it is nice for certain looks.
Now lots of people claim they love to use deli paper...I've never had any so I can't tell you how well it prints or how it compares to these other papers. If you have a chance to try some, I'd say go for it and then compare it to others. You might find you like it just great...
So there you go....other than the copy paper I think they all did a great job...
I think it's more personal preference and the finished look you're going for.