If it is a 16550 then it is fast enough. If it is a 16450 or a 8550 then you will need to upgrade. Your computer supplier can do the upgrade. Macintoshes all have sound built in and a serial port that is fast enough. More speed, more memory, more disk and ability to play sounds are all nice to have, as they make it easier and quicker, especially when viewing movie clips or listening to sound clips.
Some exchanges are worse than others, resulting in lower speeds.
Also, you may want to disconnect other telephone extensions in your house while you are using the Internet. It is best to get a 28.8 kbps modem. Low speed modems, those less than 14.4 kbps, are OK for e-mail but not for browsing the Web. Where to find a list of Internet Service Providers Internet Magazines such as Internet Australiasia and internet.au each have a list of Australian Internet Service Providers in each issue of the magazine. About once a year these magazines usually run a comparison of the major ISPs.