I�m going there for the fourth time next week.
If you want somewhere fairly cheap, you�d be unlikely to find it online. A good option is to go to the Tourist Information desk at Barcelona airport. They speak good English and they�ll ring the hotel and book for you, after finding somewhere in your price range. They make a small charge � only about 10%. Ask them anything else you need � they�re very helpful. If you come in on a late flight and find that desk closed, there are others in the city centre which I think are open later. There�s one in Pla�a de Catalunya, which is where the airport bus terminates � it�s down some steps in the square � you should see the �i� sign above it.
As for staying somewhere near the Rambla ... it�s about as central as you can get, and you can have a meal al fresco on the Rambla with some street entertainment, but be aware that you might not get to sleep till 4 a.m. because of all the bars and discos, if you�re moving on the next day!