i only went to the main page and those definitely don't look cheap. wait till you get down there to find one and just live in the shittiest one possible.
If you're going to do that get a hostel for a couple night and just spend 2 day looking for flats, BUT remember if this is your plan only do it at the end/begining of the month as that's when people leave flats otherwise you'll end up fucked, if you want a cheap flat look around Gracia, it's a little bit further a good skate into town and a 15 minute Metro ride home.
But find an area you want to live in first, the cheapest places are obviously the shitty areas, i live in Raval, beside Paral.lel it was cheap, good, and really nice, but that was living on Rambla de Raval, it's full of imigrants/thieves/gypsy's and it can be pretty ghetto, but it wasn't that bad, once the locals realise you live there they stop trying to steal shit from you and turn nice hahaha, it's just off Las Ramblas and about half the price of anything you'll find there.
Otherwise Barri Gothica is ghetto, fucking hot, no air, but really cheap and the other side of Las Ramblas, the area around Universtate is pretty good, but getting out of the centre.
Honestly get a map, have a look at where you want to be near, a Metro station is a must, then just look for that area - if you're going to search the web, remember you're renting in CATALAN, NOT SPAIN, i can't remember any of the sites i looked at but i think catalunyaonline or something like that was really handy, also remember to pick the flyers off the lappost i got a sick flat for a month doing that, MACBA and asking other skaters for rooms it good to, got a flat for a month doing that as well, you should also be able to hook up a night or 2 from someone friendly if you're lucky.
Just remember the end/begining of the month thing and the Catalan thing and you'll get a flat that's cheap and in a good part of town