Verify that they actually do clear through who they said they cleared through. More than one firm has not checked out when I have called the clearing firm to check! No I will not answer in this thread as to who - ask them their clearing firm and then call that clearing firm and verify.
Verify through their regulatory body that they are actually a member.
Read the entire contract beforehand. Anything you object to ask about. If they say "oh that doesn't matter, we can bend on that" for non-competes, lockup's , etc but won't modify that section then stop and think - that's a legal contract - it'll likely hold up so if you are not comfortable with it maybe you shouldn't sign. The contract is what will matter if there is a legal dispute down the road, a person's word on a phone call is meaningless. That'll offend some but it's true. Look that puppy over - there's alot of firms out there - you should be picky too.
Those are pretty simple checks to make before you go too far. If they are lying about who they are doing business through why would want to get yourself involved? Kinda the same as an employment background check - you should do that on them and make sure the company is real. Otherwise you just threw your deposit away. Literally.
Good luck out there & good trading