Should I pursue MBA or join a company to gain some work experience? Is work experience necessary to pursue MBA?

It will depend on which company you want to join. Your desire also plays a role here. You can do MBA later on after gaining experience. Or, you can do MBA and then go for a job.

It depends on what you decide to do, you can join the company to get experience and you can also do your MBA. But, I think the best is to do your MBA first will be a better choice because time is unstoppable. And with your MBA you will get more salary.