Salary package - Suggestions and Questions

I'll take the liberty in replying back in detail (step by step):

1. Visa - It usually takes a day to take out an employment visa from 'free zones' or 'Government Offices', however, if a Corporate is based outside of these premises, then they need to go through a 'Labour Approval', which takes about 7-8 days, and then take your visa out; total number of days to get visa in hand would be 10 max.
Once your visa is out, and you enter UAE, you need to go for a medical test, once the test result comes out, which should take a day max, your passport, along with your visa, and medical test goes for 'official' visa stamping on your passport, again, this is a 1 day job if the Corporate wills.
So basically, within a free zone, once you send them your passport copy till the date you actually arrive and get your passport stamped, should not take more then a week. Outside of a free zone, the whole process should not take more then 14 days.

2. Accommodation - I think it is best suited for you to go with company accommodation, or the facilities provided by the Company, because if you ask me where European Ex pats are, then that would have to be 'New Dubai', (anything after Sheikh Zayed road, going towards Abu Dhabi), you must of heard of places like, Greens, Barsha, Tecom, JLT, JBR, Marina, Discovery etc. These are the places you would want to settle down. A one bed flat in these areas falls within your reach i.e. 48,000 Dhs a year. You may check various sites on identification, dubizzle.com etc.

3. Car/Metro/Rental - Cars are very cheap in Dubai, it is advised for you to lease out a car on your name after you arrive here, but for this, you'd have to wait for three months, since the banks that lend out money for car purchase, needs to see your salary coming into an account for three months. Then with a low down payment of 10% you can get a car for as long as 60 months on instalments. You may want to go for 2nd cars, and not the new ones, since they are value towards money, and the new ones can never be recommended because Dubai is a place where people come and go, so again, if you want to check out the pricings on second hand cars you may go through various sites to get a feel.
Anyone working on the strip between Sheikh Zayed and Jebal Ali would love to use the Metro, yes it is cost effective and works great for professionals who work in house, behind a desk.
If you want to rent out a car for the first three months, before you purchase your own, then the rates start from 1800 Dhs per month, which can get you a Toyota Yaris, and then things go higher, of your looking for a Corolla or Camry etc. Dubai has International rental Agencies, like Budget, Hire, Avis etc. Again you can get a rental car from the airport itself.

Now coming to the tricky part of things 'SAVINGS'; It is completely on you, you may save 50%, or none, depends on the kind of lifestyle you intend to foresee. The salary offered to you will allow you to save money of course, but if you get trapped in credit cards and personal loans then that's a problem. I have seen in the past and now, that people without banking liabilities are better off here even if they make 10,000 a month. So take care of this, and you shall save money for sure.

I hope the details provided above are comprehensive, however, should you have further queries, feel free to private message me.

Good Luck pal !!

Saud