<blockquote>Hi, I am planning to apply for MSc international marketing from Birmingham university (is it a good selection?)</blockquote>
A good selection - compared to what?

In the past few years, it's become more difficult to get a work permit in the UK after your studies - you have to have a job by graduation in order to stay. And this is even true for MBAs who have work experience - and it's going to be harder for people who do other master's degrees and who don't necessarily have work experience.

For better chances, you probably want to do either an accredited MBA, or a ranked masters in management program (Imperial, Cass, LSE, Warwick, etc.)

<blockquote>Hi,
I am planning to apply for MSc international marketing from Birmingham university (is it a good selection?), can someone tell me what is the scope of placement after course? Are international students not getting priority in jobs? And suppose if after course I don't get job immediately then for how long I can stay in UK? </blockquote>

No doubt Birmingham is a good university, however I would not suggest Marketing course in the UK. Being an International Student it will be difficult for you to find an appropriate job, due to cultural change.
If you have better grades in your UG degree then you can look for more options apart from Birmingham as well.
Currently students can apply for Tier 2 Visa provided if they have job offers with over 20K per year.
You can stay in total of 16 months including 12 months of course study period.