On the internet speed is determined by the type of connection. What type of processor speed or other hardware you PC is configured with is largely immaterial to the Internet Performance.
Whether you have a fast or slow performing PC only has an affect on how fast the Internet explorer opens and how fast MSN or yahoo messenger opens. Once you get them opened quality of your communication in the messenger, speed at which an Internet page is displayed on the PC is dependent on the speed of the line. This is what is actually called the PCs performance while using the Internet.
To give you another example, speed at which a 50 MB file is downloaded from the Internet depends singularly upon the bandwidth of the connection and does not have any connection to the PC performance. These are simple things however some people miss the point. Hence it is being emphasized.
Taking a 56Kb modem as the basis for a connection, it must be understood that better performance could come from ISDN 64Kb, ISDN bundled which would give you 128Kb. Next option would b to go for DSL or Cable based connection which can come in bandwidths of 256 Kb, 512 Kb or more.
need for speed is ever increasing. people want to do more downloads, more streaming video, do more browsing. see others over webcam. There is no doubt that more bandwidth is preferable to less. Everything that relates to the net begins to be better with higher bandwidth. This is especially true for downloading etc.
Another thing we would like to add here is the fact that with permanent links like DSL, cable etc, your chance of getting hacked or otherwise attacked over Internet increases. Hence you must ensure that the firewall is turned on and configured well.
Next : Startup Programs.