I always wanted to check out the Hellboy/B.P.R.D. universe. Pretty much all the characters in it are quite unique and weird in someway.
What mini series (solo and team) would be a good starting point?
For Hellboy - going back to the start is probably your best bet - the first trade Seed of Destruction is a great read and it just gets better from there. The good thing about Hellboy is that most of the trades are fairly self-contained so you can pick any one up and still enjoy it.
There are a whole lot of BPRD trades and it may seem daunting at first, but just jump in and pretty soon you'll be as hooked as the rest of us. I found BPRD: Being Human to be a great intro to the characters.