TRAVEL TO U.A.E.
If you flew in for an interview, you would have come in on a Visitor Visa - this is automatically provided at the UAE airport - no prior visa application is required. If you then went back your home country to e.g. give two weeks notice - and / or to get attestation completed - upon flying back into the UAE to start work, your employer should have a 60-day Employment Visa waiting for you at the airport.

GETTING RESIDENCY
Your employer, as your sponsor, is required to obtain your Residency Visa from the NRD in e.g. Abu Dhabi, Dubai or Sharjah. This will involve going to a government clinic for public health protection purposes i.e. to ensure that you are free of TB and HIV. The medical certificate enables your employer to get a Labour Card a.k.a Work Permit for you, the last pre-requisite for residency.  The Residency visa is a fraud-protected insert, pasted into a page within your passport - make plenty of visa photocopies as many UAE transactions require proof of residency!! This visa is issued every 3 years up to age 60, annually after that.

Once you have your residency visa, you in turn will be responsible to get such a residency visa for your spouse as their Sponsor -  note it doesn't authorise them to be allowed to work. Employers will often aid you with the spouse process too.

EMIRATES IDENTITY ID
The UAE hasintroduced a new ID card for nationals and for expats - similar to the US green card - which is meant to replace all  other separate forms of identity. Once better known, it could eliminate the need to carry your passport.