Which bank and broadband? (Budapest)

Hello,
We just moved to Gyor from the UK.
Our income comes from the UK and it seems that if we take money out from our UK account here, we get a rubbish exchange rate. Exchange rates also seem to vary by ATMs. Yesterday we tried several ATMs one after the other and the exchange rate we got was between Protected content - Protected content to 1 GBP. Nowhere did we get the Protected content exchange rate one gets for cash at the moment!
We were wondering if anyone is in the same situation (income comes from the UK) and what bank account is best to use, where we could transfer the money every month and either withdraw it in HUF at a good exchange rate, or withdraw it in GBP so we can exchange the cash?
Also, which broadband do you recommend? We need a fast, stable broadband that we can use as a WiFi hotspot too.
Thanks very much in advance for any help,