Hello.
Wich is the most beautiful and the cheapest hotel in barcelona?

Can't give you a definitive answer but there are plenty of websites where people who have stayed at various hotels give their true and honest opinions
Reviews of holidays, hotels, resorts, holiday and travel packages - TripAdvisor (http://www.tripadvisor.co.uk/)
Is the one I use whenever I go away and it is usually spot on!!

By the way Barcelona is amazing

I am visiting porugal and spain. I am confused on where to stay in barcelona. WE would be in spain for six nights and would like to know about barcelona city and a nice beach resort near by.