yeah, long screws is whats done when layering drywall, also glue. Then you need to extend electrical boxes, door and windows jambs. My suggestion is to usually rip the old drywall off, it gives you the opportunity to add or upgrade insulation, add outlets, correct issues done in previous work, etc.
You may want to shop around for a drywall contractor. When I did my basement I found a guy to do the entire thing, ready for paint, including materials for not much more than I could have bought the materials myself. See if you can find companies that only do drywall, my guy does mainly commercial projects but was hungry for the work. They delivered the drywall on Monday and I was painting on Saturday. This was a 1400 sq ft finished basement, including ceiling and it cost me about $2600 as I recall, or about $25-$30 per sheet. Of course I didnt have old drywall to remove, my walls were straight, etc.
You could tell the contractor you will have the old drywall off and everything cleaned up and his price will be lower. If you also need to pay the guy to rip the old off then it will cost a lot more.