Imagine your Internet access being at least 5 times faster. That's how much faster even the slowest broadband is compared with dial-up. Imagine how many websites you'd be visiting if your Internet access was that much faster. Broadband access will do it for you.
Broadband Internet technology is usually ADSL, cable or wireless, with ADSL being the most common. Irrespective of the type of technology for your broadband access, you'll have some choices to make.
One of the choices will be your plan, covering such things as your access speed, and possibly a download limit. Just remember that even the slowest bandwidth offering of 64K/256K will seem like greased lightning after dial-up.
Another choice you'll have to make will be the type of modem. Make sure you choose a modem with a router as part of your broadband setup, or buy your own. It doesn't cost much more to get a modem / router, and you'll at least have some level of protection from trojans and other nasties out there on the Internet. Don't let the friendly people at your local ISP talk you into a straight-through modem because it's cheaper. Yes, the friendly, helpful people at your local ISP. Sorry, I don't understand what you mean by "droids on the helpdesk from hell".
Once you've experienced Broadband Internet access, you'll hate the idea of going back to dial-up.