Essential Constantine comics?

I'm a very big fan of the Constantine tv show and I've been meaning to read the comics for a while now, but what should I read?

I know that he's in Swamp Thing, do I have to read those first as it's his first appearance? Are they good? Also, do I read Hellblazer or Constantine? Or both? I know Hellblazer is supposedly better and those are the ones I'd intended to read, but there are three hundred issues so I imagine that that would be quite expensive, wouldn't it? I presume you can't skip any?

In addition, if I read the Constantine comics, do i have to read The Justice League Dark ones? I wouldn't mind reading them, but guess I would then have to read whatever came before or is relevant to them.

Finally, which comics have the crossover with Batman and what do need to read to be able to read them? I've seen bits and pieces of them and they look great.