For broadband ISPs, there are several important factors to check, including reliability, speed of connection, how many other customers share the total bandwidth (the Contention Ratio), and of course, cost. Most charge a set-up cost, and many have a minumum contract period, so be careful you don't get locked into a poor deal for many months!
Sites like Switcher.ie can be useful to see what's avaible in your area.
http://www.speedtest.net/ can show you how fast your currest ISP is.
Data Allowance and Dat Caps: Check whether your ISP offers an “unlimited” or “unmetered” service.