Your best bet is to probably send your UK partner over here a couple of months ahead of you. Unless you both have some pretty substantial savings, he'll need to secure a job to prove that he can afford to support the two of you (and your child/children, if they're coming over, too) and that you'll have a decent place to live.
I did exactly that just these last few months and everything went perfectly. I came over to the UK two months before my wife to get a job and find a place to live. Before that I had never lived in Britain, but it was easy to find a job (not the best job, but one which ultimately satisfied my wife's visa requirements), and it didn't take more than three weeks to find a place to live.
In addition the the usual items req'd by the application, my wife and I sent them a letter from my employer here in England and a copy of a lease with both our names on it (I was lucky enough to find a landlord who did that for me, after I told him I'd need it for the visa app.). I did not even have any bank statements or pay stubs yet, just a letter from my boss. Because of that I was nervous that there'd be a snag or at least a lengthy interview, but we got the visa in the mail with no interview.
Other than that, we just sent them the normal stuff that proves your identity and the circumstances of your relationship.
I came over Sept. 9th, and we had the visa in hand Nov. 29.
I wish you the best of luck!
