Palms is a really great hotel actually, it is one of my faves in Vegas (second fave is Venetian) it's just a really happening hotel, with great dance clubs and overall vibe...if you guys can afford to stay there I would. I also really love Palms Place, which is part of the Palms but they are studio apartment style, quiet, roomy and very nice.
Cabs can get pricey for getting around Vegas, so I wouldn't suggest staying on the strip unless you have a car/will be renting a car in Vegas. It might be worth while to all pitch in and rent a car whether you decide to stay at Palms or elsewhere because if you have never been to Vegas, there is so much to see and do and a car will make getting around to see everything so much easier!
If you do decide to stay on the Strip, some great hotels are Treasure Island, Mandalay Bay, Venetian, Planet Hollywood, Cosmopolitian, New York, NY and MGM grand.
Now if you are looking for economy and clean and comfortable rooms on the strip check out Bally's, Tropicana or Harrahs.
As webby mentioned, downtown Vegas is cool and fun especially at night...I would suggest the Golden Nugget hotel if you choose to stay downtown, as Golden Nugget is the nicest hotel out of all the downtown Vegas hotels and has a killer pool. HTH!