There are numerous types of equipment configurations.  A good rule of thumb to remember is that you should have as fast a modem and processor as you can afford and as much memory (in your PC that is) as you can afford.

Lets start with the basics:

Standard Modem

There are many models and types of modems on the market today.   In order to utilize the net to its fullest, you will probably want to get yourself a 56k modem.  Now that's not to say a 33.4k or a 28.8k modem won't serve your purpose, however, once you really get into trading you're going to want all the speed you can get.  The advantage of the standard modem is that it uses a regular phone line.   You will probably want to get a second line for this.  Make sure that you do not get the call waiting feature as it can interrupt your connection if someone tries to call that number.  If you use your primary telephone line, get the code from your telephone company to disable call waiting.  Add this code to your dial number for your ISP.  In most locations the code is 70#.  Therefore, you will need to add 70#,   (Seven, Zero, Pound Sign, Comma) to the front of your dialing string.

ISDN Modem

The ISDN modem provides speeds of either 64k or 128k.  However, it requires a special telephone line from your Telephone Company.   They are better than the standard modem but not as fast as a cable modem.   However, they are very reliable.  Prices between the various telephone companies vary greatly from flat rate service to measured service.  Make sure you know the complete pricing structure, both installation and monthly fees, before you decide to order this service.

Typically, you'll be using the ISDN line locally to your ISP.  Therefore, when you order your line you can specify no long distance carrier.

Also, once you start to get you billing, check to make sure that some third party long distance service hasn't added their service to your line without your permission.

Cable Modem

Cable modems hook up to your cable TV system and provide a high speed connection to the internet. Typically, the speed is 10Mbps however, the more users on the cable system using the service at the same time can reduce the overall speed and performance. Keep in mind that not all cable TV companies provide this service. 

Cable Modems

The DSL modem provides speeds from 64Kbps to 1.5Mbps depending on the level of service.  DSL requires the installation of a special phone line from your telephone company.