First, you need to determine why you want a laptop. What is it you are hoping to do with it. You'll need to consider different options for different purposes.
I'm confused as to why you'd want to take it with you to the park, coffeehouse, etc. Are you planning on surfing the net while out and about? If you need to work, why would you be at the park or coffeehouse? Just to be doin' the trendy thing? Or for business meetings?
As far as getting on the internet with a laptop, most come with built-in modems. You can dial up just like a desktop computer. Just plug a phone line into the jack and into the wall.
To add on to your home network you have a few options. If you are working with two windows machines you can an ethernet card (standard on most, but not all computers) and connect your machines through that and a hub with ethernet cables. You'll need to set up your machines; there is a wizard in Windows 98 that will help you do that. (You'll need the ethernet option if you plan to hook into your network at work.) You can actually piggy-back a Mac onto a windows ISP-link, but its a lot more work without the router, and NOT for beginners.
Your best option for sharing internet access is to use a cable or DSL provider (for speed!), a cable modem and a router. A wireless router and a wireless access card in the laptop make this even sleeker. (I can look up recipes from the kitchen or check my email while I'm outside enjoying the weather.)
Some things I considered before switching to cable access were the cost of a second phone line (including taxes-$31) and the cost of the ISP I was already using ($19). It actually came out cheaper for me. I did purchase a cable modem and router, but I considered them long-term purchases. The price for those items has dropped significantly since then, too. Often you can find the cable modems "free after rebate" when you sign up for cable internet service. Also, try to sign up for the service when they are offering free installation, or ask for it when you call.
Since you're in California, there are probably lots of coffeeshops with internet. You must have a wireless access card installed to use them.
Some other features to consider: screen size, RAM, processor speed, hard disk space, weight, CD/DVD drive, USB ports, firewire ports, and operating system. I went for a model that had the DVD drive, that way the kids can watch movies on long trips. I didn't feel the need to burn CD's on the go, though.
You really need to think about what and where you will use the machine for. For most people, they are really just toys (nice, expensive toys). For others they are a necessary tool for work. How much machine you buy will depend on your uses and your budget.
