Yes, you basically have it correct. Your cable modem will plug into your wireless router, which can (and should) be purchased with "hard wired" ethernet ports so that any desktop/tower computers can connect without the need for installing a wireless card. For all laptops, ethernet devices (TiVo, etc.), and desktop/tower computers too far away from the router for a hard wire, they each will need a wireless adapter.

As far as security, there are a number of proactive things you can do, but keep in mind that even with WEP, WPA, MAC address restrictions, etc., a wireless network is still fairly hackable. Enabling these things will prevent the casual hacker from getting into your stuff, but if you've got a particularly conniving or malicious neighbor with time on their hands, your stuff may still be at risk. I would suggest, if you're at all paranoid about things, to leave at least one computer hard-wired to the router and use that computer for all the credit card transactions you do, as well as any other transactions that involve sensitive and/or personal data.

Linksys is a good consumer-level brand as is Netgear and DLink. I've had experience with all brands and they each have their positives and negatives. When you're shopping around, note specific model numbers of the hardware you're interested in. Then, just type the model number into Google and you'll see many reviews come up. This should help you identify which devices fit your needs.