They were hunting "four things and a lizard", one of which apparently had nested in London with the eggs about to hatch. It's left intentionally vague. (I personally imagine some kind of monster hunt staged on Earth by some irresponsible alien event organiser. Do you want that to be cleaned up by the Judoon?)
We're never told whether Ten and Martha ran into the Weeping Angels by accident or by design. You'd expect the Doctor to look through the file given to him by Sally, and then go where he needs to go in order to avoid a paradox... But then again, this is Ten, and he obviously didn't plan ahead for an extended stay in 1969, if Martha had to get a job to keep them afloat.