FWIW -- I think it depends a little on who you are (e.g., how famous or bestselling) and on the work itself (how high-concept/commercial/genre). And maybe even on your agent/house. But that said, or if you're a debut author, you're likely to hear that the first book has pretty much got to stand on its own regardless. Or else your two books may need to be combined into one longish one -- which might be a good option for you?
I was in more or less this situation, though I had 3 ms's to start. But the first one was not considered self-contained enough by itself (I thought it was, but others didn't), so the first two were combined (with some cuts to make it a reasonable length). And the third book has become the sequel, though the new 1 and 2 were sold separately. And since now the third book of the trilogy (originally it would have been a #4) is drafted and we hope to sell it, too, so it really will become a trilogy, but that will depend at least in part on sales of the first two.
Repeatedly I heard during this process, directly and indirectly, "Each has to stand on its own and sell on its own." YMMV.
Of course, I've read first books of trilogies that in no way stood by themselves, but I think that's easier to get away with if you're already a marketable name (and there are thus essentially guarantees that a second/third book will be bought and read. If you're not a platform in your own right, the first book might not sell well enough to prevent them from bailing on the second/third.