I have a masters degree in computer science and 12 years experience developing software. I am moving to warsaw and will be looking for jobs in my field. I have around 5000 euros with me and want to be able to settle with this much money. What can I do to survive with this much money, save on rent, and be close to the city center so I can go for interviews etc? I also want to buy a cheap used car. Any advice is appreciated.
You won't need a car in Warsaw. Public transport is very good, if a bit overcrowded at times. A car is a total waste of your valuable savings and if you buy a cheap one, you're asking for trouble.
There are plenty of pleasant and affordable places to live within 15 or 20 mins of the centre by tram. The actual centre as in Śródmieście I wouldn't recommend due to the volume of traffic and the filthy, polluted air.
You'd actually be better to look for a job and try to do Skype interviews before coming to Warsaw as you can then look for a place to live in or close to the neighbourhood where you'll be working. Many software jobs are located all over the city, not just in the city centre.
There are loads of threads on the forum about moving to Warsaw so take a look at them.