More information on your diving and future diving plans would be helpful.
Here's my quick $0.02 on the questions:
Air Integrated
Pros: With air integrated into the computer, you have an all in one dashboard. One less hose (if you don't carry a back-up SPG).
Con: Additional complexity, potential failure point, expensive, and some first stages may not have space for the transmitter.
My recommendation: Air integrated is not necessary and not worth the additional expense. There are simple formulas to determine gas consumption, and after a few dives monitoring your SCR/DCR you'll know how much you use.
Mixed Gas (assuming Air and Nitrox only)
Pro: Future proofing for many divers.
Con: Additional cost.
My recommendation: Get a Nitrox enabled computer. Usually only a few dollars more, and does provide a lot of flexibility. Beyond a nitrox enabled computer, I'm not so sure. Actually started a thread to see if it's possible to
Future Proof with a multi-gas computer.
Counsel vs Watch
Counsel Pro: Won't loose your computer.
Counsel Con: Can make the counsel bulky.
Watch Pro: Depth and Time easily available. Convenient if you need to manage depth (eg. safety stop).
Watch Con: Another piece of gear to remember.
My recommendation: Watch. I like having the depth and time readily available, and with arms in front, the computer is always in or near my field of vision. Great in situations were I have to multitask and manage depth.
New vs Used
New Pro: New and shiny
New Con: Expensive
Used Pro: Save money
Used Con: Unknown condition (always buyer beware)
My recommendation: This is personal, but I have no issues buying a simple Uwatec Bottom Timer or a nitrox computer with replaceable batteries. Need detailed pictures and confirm that the seller is reputable.
With regards to buying a computer, I like one with an intuitive user interface - something that I don't need to read a manual for. Unfortunately, not many dive computers fall into this category for me. But I could just be thick headed (and judgmental) since I help build software products.