About internet
The company doesn't provide you this service, but if you are lucky to have flatmates that have already installed it, and are willing to share then you are good. If not, unfortunately it will take you aproximately 1 month to get internet. To get the service itself it takes 2-3 days, but in order to do that you need a passport, which you will have it back only after approximately 1 month from your DOJ. Prices start with 300 dirhams/month
About mobile phones: you can get contracts, I think you only need a passport copy for that. For the prepay packages I know it for sure. It is very cheap, for example you can get a package for Blackberry for 78 dirhams until 300 or so. Or just a normal prepay: 0.30 dhs/minute within Dubai, 0.60 dhs/minute international, 0.18 dhs/sms within Dubai ...this are more or less the prices, You could search for Etisalat or Du, the two mobile services providers.
Any other questions...feel free to ask!