Lag is your number one enemy when online gaming. You could also do with giving yourself some spare bandwidth to cover off use of the line by anyone else you share it with.
While some games may require more bandwidth than others, you also have to account for variations in the service at different times of day.
While you can get gaming, theoretically, by using cheap broadband running off ADSL, it's recommended that you go faster than 3Mb, if available where you are. The first step is to take a broadband speed test so you know where you're at right now. 10Mb (normal ADSL internet) roughly translates into download speeds of 1.25MB per second, while 35Mb fibre broadband takes that up to over 4MB per second.
Mb - sometimes displayed as Mbps - means 'Megabits per second' and is an easy way to compare the average speeds offered by broadband companies.