In a few months my boyfriend and I will be moving into a new apartment together....
You actually have two separate situations: a new home and introducing new pets.
Let's start with moving to a new home."Moving can be a very stressful time for families and pets alike. Pets often pick up on the stress and can certainly display behavior changes related to this stress during the move. To minimize stress on pets, it is best to keep their routine as consistent as possible as long as possible.
During the actual packing and moving process, it may be best to board your cat which will minimize risk of escape while the doors to the house are open. If your pet is going to remain in the house, confining them to a quiet room with their favorite belongings may be helpful. Ensure they have current collars and tags, in the unfortunate event that they do get out.
Now for introducing the two cats. If possible, provide each cat with her own space where her food and litter will be housed. Keep them separate at first until they become use to the new surroundings. After a few days,it's time for a face-to-face meeting. Expect some fluffed tails, hissing, and growling. Keep a spray bottle filled with water handy in case an actual fight develops. Don't leave the cats alone until you're sure they have accepted each other. In time, you may be able to move their food and litter boxes closer together. I do recommend letting each cat keep her own litter box though.