Depends on your lifestyle, how many people you support, etc. Sounds like enough if you live in one of the outlying communities. House and apartment prices are sky high, and going up about 15% each year, and rents keep going up too. If you want to buy, the interest rates are about 3% to 4%, I think, so it can be done.
I recommend you check out Alcobendas, Colmenar Viejo, Hoyo de Manzanares and maybe Guadlix de la Sierra. There are also many more communities to the east and north-west of Madrid you might like to check out. They have public transport. Driving is difficult (not to mention dangerous), parking is next to impossible, although parking in a garage is often easier. I have many kilometers of experience apartment and house hunting here and would be glad to give you some advice, but the best advice is to get a car and cruise around looking for for rent or sale signs ("Alquiler" or "Venta"). You can also check out Segundo Mano, which has a huge listing of the same.
You can pick up a decent used car, usually directly from the owner, but get it checked out. We bought our Citroen Saxo from our landlords for about 3000€ and it has been a great car.
You will be way, way ahead since you have a job offer. You will be able to get Residency and Work permits without hassle. Lucky you. You will be making more than twice as much as the average Juan(a). Personally it sounds like a great deal. Do they have any openings for a Systems Analyst/Programmer? (Seriously!)
Good Luck, and Bienvenidos a Madrid.