IMHO, the original CSI is still the best. Though it's had a lot of turnover of characters, you probably don't really need to catch up on any major plot arcs, since there really aren't any that span the whole series. It's very episodic.
Of the other two, I find CSI:NY the better - it started off poorly (bad character writing and boring acting), but it's really gotten its act together the last few years.
CSI: Miami is just ludicrous. I only watched the first few before giving up.