http://www.habitaclia.com (only in Spanish)
http://www.fotocasa.es (you can choose English language)
http://www.idealista.com (you can choose English language)
http://www.key2bcn.com (in English; great site, but prices are higher)
Once you have found a flat that suits for your, phone and ask for appointments to visit (this is the most troublesome part for non-Català or non-Spanish speaking persons). Be prepared to pay before you sign the contract itself. Most of the rentals are managed by agencies, although a few are taken care directly by privates. It is common to have to pay 2 months guarantee (fiança) + 1st month payment to sign the contract. Moreover, agencies typically require payment of honoraris: (1 moth rent or 10% of 1 year rent)+IVA(21%).
Basic (and specialized) health care assistance in public hospitals, health centers and pharmacies, is provided through CatSalut. One should request the “Tarjeta Sanitaria Individual (TSI)” at the health center of neighborhood of residence, which can be located here:
Bring in the usual documentation and this form dully filled and signed.
In the Physics Building there are offices of Banco Santander and La Caixa. They both have a good coverage of the city in terms of ATMs. They speak some English, which is not usually the case and can be particularly useful. If you just landed in Barcelonaa you can use the department's address to open the account. Have your NIE with you (or your passport if you decide to open the account before getting the NIE) and some little cash with you to open the account. Once you have a phone number and home address tell them so that the account gets upgraded to offer better interest rates.
A good option is to go to a nearby office of Movistar, due to its good coverage (other options are Vodafone, Orange, …). You can find nearby Movistar shops here:
You will need the NIE and bank account number for a proper contract (cheaper than prepaid-card).