I was given a cheap, open back banjo a while ago and it is still the one I still use. I got a book/cd from Tony Trishka of fairly simple tunes and started learning the more "scruggs" style. I never really got any good at it -- it was before I got into recording and I never played with anyone.
Then I lost one of the finger picks and now when I play banjo, I get the banjo chord sheet out and just sort of flail away with my fingers (ha, ha). Probably mostly guitar style fingerpicking, though. I think the best bet would to be try and learn the 3-finger scruggs style (open back is fine for that, too). It is a good place to start. Actually though, I think you have to use what you know and just do it -- do you really want to spend two or three years becoming a proficient bluegrass picker? Here is me stumbling along on banjo:
https://soundcloud.com/kevin-emmrich/shout-it-outA ukulele is always a good idea for a new instrument, too. ... and why not, here is me on my daughter's uke -- I have played it maybe three times:
https://soundcloud.com/kevin-emmrich/slightly-out-of-phase . Again, I just get the uke chord chart out and do the best I can.
Edit: Of course then there is Scott Avett of the Avett Brothers. He started out with the 3 finger scruggs style, but now is sort of a hybrid player and mostly does stuff in support of the song. Here is a good example:
Laundry Room. He is always tuning that dang thing, though!