I'm not a hybrid queen, but I do print out from time to time. Here is a thread from a while back that might help with your paper question. Hopefully the real hybrid girls will pop in with more tips!
Yup - you can print out your digi elements... majority of us print on photo paper or presentation paper (found at most office supply stores)... the results give to truer coloring as you see on your screen. Cardstock is an option, just be aware that it can really suck up the computer ink and may look "dull"... you can always take your design to a print shop and have them print it for you, too.
Just let us know what other questions you have... I always look for an opportunity to talk a person's ear off about hybrid...