What are the pros and cons for going into the EU?

The benefit is mostly economic. No tariffs, means lower cost for international business. Easier border crossing and more lenient working permits for EU citizens encourages people to move where they and there work are needed and results in greater flexibility.
A unified currency (€) creates a more stable economic landscape and removes the cost of currency conversion, making international business more attractive.
These sort of things.

The UK joined the EU in 1973…
One of the reasons the EU was created back in 1952 (it was then called the European Coal and Steel Community), was to prevent another major European war from happening. The economic successes ‘spilled over’ into some political fields as well, and the countries integrated more and more. Other countries looked at this and wanted in so they could also reap the benefit of a larger market with no internal boundaries. Nowadays, the EU is much more than economic cooperation, but the internal market is still seen as the cornerstone of European integration.

It is also an enormous cultural benefit. The EU makes it much easier to experience at least parts of other cultures, making people more open minded.

Why should cities like Manchester join the UK and not be totally independent?