Were the Potters rich like the Malfoys or upper middle class? And what happened to Sirius' family fortune? Is it all Draco's since he's the only heir (others are either dead or disowned)?

The Potters were rich - James was an only child. Their vault was full of gold.

As for Sirius' wealth, it must have gone to Harry, as his house did. So why not the rest of his fortune ?

Successorship laws seem different in the wizarding world. Apparently, you may disown heirs while in the Muggle world, you can't or only for a part. So we may think that any witch or wizard can dispose of their wealth as they wish. Sirius must have planned to have everything he has left to his godson Harry.

I agree with LadyN when it comes to the money. Another thing to add about Sirius' fortune Fletcher did steal several items from the house so I'm sure that's where some of it went other than that I completely agree with LadyN when it comes to everything she's great with answers =)

I don't think the Potters were as rich as the Malfoys or the Blacks, since there is no mention of them ever living in a place like the other two families did. James and Lily lived in a family house while the Malfoys lived in a manor with a huge estate and the Blacks in an antique Londoner house. I think they were upper middle-class which, of course, means quite a lot of money as well.

As for Sirius's fortune, it passed to Harry. In the chapter Will and Won't Dumbledore tells Harry about Sirius's will.
"You add a reasonable amount of gold to your account at Gringotts and you inherit all of Sirius's personal possessions."

It was only the house, Number 12, Grimmauld Place that had such a tricky tradition of passing on. Otherwise everybody left their money to whoever they wanted. Sirius tells Harry in OotP that he inherited a nice amount of money from an uncle who always liked him, that's how he could buy his own place.

As for the gold of the Black family, of which Sirius was clearly disowned when he left his family at the age of 16, I think it went to Bellatrix and Rodolphus and with their death, to Narcissa and thus it ended up in Draco's vault, as you say. But that's a mere guess.