Running a query which gets posts from whatever page you're on

I need a query that’ll get the posts for the category, search page or perhaps archive page that you’re on. I’m working on a pagination system and I have no idea how to do this. I’ve tried a bunch of things.

What I’m looking to do is get the total number of pages (10 results per page) for the category you’re in. Also I’m looking to get the posts for that category as the second page. It is an AJAX pagination system, so that might make it trickier. Any help at all is appreciated.