Do you want DSL (i.e broadband down a phone line) or mobile (o2 , meteor, vodafone ,3) or wireless (Clearwire, Irish Broadband) ?
What speed do you need/want ?
There are plenty of options - but generally the most consistent will probably be down a phone line. The wireless and mobile coverage can be patchy - it depends where you are located.
Some telephone providers include free landline off peak calls in the broadband packages - so the price may not be as bad as you think. UTV do 1Mb and all off peak calls in Ireland and UK for just over 39 a month including line rental .
Smart do 1Mb down a phone line for 33.13 a month (no free calls)