Poor new cat.

So we brought home another cat today... That makes 2 in the apartment and one still in the ceiling... I have only known her for a few hours but I am already in love with her. She is a dilute calico named Cala (I dont really like her name.) Her previous owners, I dont even know what to say about them. She has an infestation of fleas, and I stress infestation. This poor cat. SHe is also pretty overweight. I felt so bad because the second I brought her into the house I gave her a flea bath. It appears that they are all dead. But I just want to see what else all you guys think I should do. I also could not get all the dead fleas out of her fur with the comb so she is leaving them everywhere. I have to practically follow her around with the vacuum. I am asking your advice about flea control and dieting. I just want to get this poor girl healthy. I will post pictures as soon as I can take them. She already seems comfortable in my apartment. My kitten isnt very happy though and is watching her every move.