First, welcome to the hobby.
For paints, pretty much anything you would use with one company's minis will work with another. Personally, I prefer a blend of Delta and Reaper Master Series, which I use for all of my minis, not just BattleTech.
Also correct me if I'm wrong, but aren't all BT minis (except the ones in the box set) made of metal/tin/pewter/lead/whatever? How prone are they to breaking and chipping off bits of metal? How about chipping the paint?
MOST mechs are lead-free pewter, but some of the older 3025 sculpts (pre 1992, iirc) are lead pewter. There were also plastic Mechs that were available in some sets (3rd Edition box, CityTech 2, PlasTech). Depending on your paint, a good primer is recommended. (and good hygiene practices when working with leaded metal)
Aside from dropping Mechs, breaking really depends on the type of glue used. I use Duro Superglue, and ship painted Mechs all over the world. Very rarely do I hear of one breaking in transit. Admittedly, I do pack them tightly for shipping as well.
Chipping (and rubbing) depends on handling, like any other type of gaming mini. Oviously, the more it's used, the more likely for chips and rubs. A couple layers of a good sealant, like Krylon Matte, should help preserve it.
Some good sites to help you get started with both canon and non-canon color schemes are:
http://camospecs.com/http://www.heavygauss.com/Index.htmlhttp://www.myrnnyx.com/Also, check people signatures. Many of the artists have links to their own galleries.
Happy painting.