Hi poppy!
We booked with Thomas Cook Signatures but that was because we had to fit Dubai in with a trip to the Seychelles and Mauritius and they offered the best price for that. Expedia seem to have some good offers for Dubai and we're booking with them for Feb you could also try
http://www.dubai.letsgo2.com for package deals. Just shop around and if it's cheaper to book hotel and flight seperately then do that as many hotels will include transfers.
There is alot of building work at the moment but if you stay at the right area of Jumeirah Beach there's no building work at all - Mina A Salam, Al Qasr, Jumeirah Beach Hotel, Burj Al Arab, etc. I believe the 'worst' area is further down the beach where they're building Palm Island - near the One and Only Royal Mirage.