I am so sorry you lost your cat. It is very heartbreaking.
Thank you for wanting to bring in other kitties. You will be thanked many many times over.
What ages of cats are you looking to adopt? Is your girl you are getting from relatives just overly affectionate with the other kitties or is she aggressive with them? Not necessarily a bad aggression but rather she is so aggressive in playing that the other kitties get irritated easily by her?
If she is play aggressive it would be wise to adopt a kitty with the same personality. It would not do to adopt a kitty that is older, quieter, and has no interest in play as this would lead to a lot of stress on everyone's side.
My suggestion, and I know others will have differing ones, is to bring them both in at the same time but, and this is a big but, put them in separate rooms that are close together. This way they can sniff each other out, they are aware there is another cat around but they can't hurt each other. The absolute worse thing you can do is to put two cats together from the get go and expect them to get along. It very rarely works out.
You can keep one in a room separate, the other allowed free run of the house for a day or so. Then switch. Allow them to get used to each others' smells and sounds before introducing them face to face. Seeing as one comes from a multi cat household and another one will be coming from a shelter environment they will both be used to having other cats around. This should only help to smooth over the introductions.
My favourite site for introducing cats is:
Good luck and ummm....... we like pics here.
One more thing. You may want to give your house a total cleaning to rid it of your lost kitty's smell before bringing home the other kitties. It will only lead to confusion. They will be looking for a kitty who isn't around.
Please don't be surprised if your original one does eventually surface.