Once I removed the old tiles is there anything else I should do before I lay the new ones?
It should be ok as long as you sweep it and mop it.
Make shore to remove all thinset from floor before installing new tile
If you're removing ceramic tiles, you want to make sure that the new ones will bond to the cement subfloor. To check this, after the tiles are removed, acid wash the concrete floor with one part of Muriatic Acid 15 parts of water....BE careful. The floor should sizzle a little. If it doesn't, you will want to remove any adhesive that is still on the floor, and that's not easy! OR, go to a tile store in your area, or Home Depot, and tell them you need an adhesive that will bond to mastic that is still on your cement floor. If you're removing vinyl tile, the existing mastic shouldn't be a problem, but be sure to remove and clean any debris that might get sandwiched between the old and the new mastic.