Freedom! Free from Madrid's suppression, unfair policies. Control their own fate including army, finances, education, etc. And mind you, Messi won't be persecuted again and again for his tax issue. Same as Neymar's transfer issue as well.
Absolutely nothing.
There is no suppression of Catalunya today, the days of Franco are long gone. The reason many in Catalunya want independence is because they naively believe that it will result in economic benefits, even though today, Catalunya and the Basque country are more lightly taxed than other Spanish regions and do in fact enjoy a great deal of autonomy.
Having said that, the chances of Catalunya of gaining independence anytime soon are quite slim in my view. For the following reasons:
a) The Spanish Constitution does not allow for something like that to happen. Madrid has law on its side. It was generally understood after Franco died that Catalunya and the Basques would enjoy considerable autonomy on the proviso that they would not be able to secede.
b) The EU will not approve of it. This has grave economic implications for Catalonia.
c) NATO (see: the US Empire) will also not approve. NATO does not want to go the way of the Warsaw Pact. It may very well suffer a similar fate one day, but it won't be in the immediate future.
But, since you can never be sure in history, in the case that Catalonia secedes, I would like to see a European Super League. If that is not possible either, then I would like Barca to join the EPL for the very obvious (and massive) financial advantages of that league. Imagine the sponsorship deals we could get by playing in the EPL!