Things to watch out for

• Use a firewall! Now. Do not wait. Do not pass go. Do not collect $200. Unfortunately the Internet has enough bad apples in it that you are nuts to connect any machine to it without a firewall. Windows systems are particularly, but not uniquely, vulnerable. You can buy NAT (network address translation, or IP masquerading) router/firewall boxes for well under $100. In addition to providing protection to your computers, they also allow you to connect all your computers to one provider, via Ethernet cable, wireless, or more obscure technologies.
• Make an educated guess as to the likelihood of your provider's survival. DSL providers especially are dropping fast. Check out dslreports.com.
• If you care, make sure you know both the downstream and upstream bandwidth.
• Make sure you understand the restrictions on use. For residential rates, many providers restrict what kind of servers you run on your computer, and whether you are allowed to run NAT to give a high speed connection to all the computers in your house. I can understand restrictions against, say, a 10 person office or a commercial web server in your home at residential prices, but preventing you from connecting one or two extra computers so family members can share the connection, or preventing you from putting up a web site containing photos from your last vacation, is just silly and bad business. You may be able to negotiate this restriction away with some ISPs. Some ISPs follow a "don't ask, don't tell" policy, that's probably ok. But if they explicitly forbid it, go elsewhere. Even if you don't have a home network now, you may want one soon.
• Find out what commitments you need to make. Some DSL providers demand a one year commitment or more.
• Find out about pricing. There may be an up-front cost for equipment and/or installation. Then there's the expected monthly rate. There also may be other taxes, fees, and other cruft. Make sure you know all the costs. You may be able to haggle about the up-front costs, and many providers provide rebates as promotions.
• Find out what bandwidth and pricing you can expect for your house. Some DSL providers offer great looking deals, and then tell you that you don't qualify for some rate or speed because you are not close enough to the CO (like me).
• Search the web, usenet or dslreports.com to find other people's experiences with any provider you are considering.
• If your provider offers a choice between renting and buying a cable or DSL modem, consider buying if you plan to stay with the same kind of provider for awhile. On the other hand, cable modem and DSL modem technology is advancing pretty quickly, so assume that you may want to replace it, like your computer, in a few years.