Simplest way to find you MAC address is System Preferences/Network and then it's listed under the "Airport ID" heading.
(Here follows a bit of a stream of consciousness, owing to a bit too much beer on an empty stomach), and is all somewhat of a simplification. Regarding security, it depends. If you live more than a couple of hundred yards from anyone else, then I'd not worry at all (unless you're a Famous Person). If you're in a block of flats surrounded by teenage computer nerds, then it's more of a worry. The level of risk depends on many things.
I'd say: Set a decent access password on your router, so that if someone gets in, they can't lock you out of your own network. Then try to get some kind of security running somehow. Now that you've connected, try to turn on some level in the router: pehaps WEP, or ideally WPA. Reboot everything (router & computers) & check it all still works. Swear a bit if it helps.
I wonder if the password thing might be a misunderstanding between what WEP & WPA reqire: Generally, if you specify WEP (Which is an older standard), then keys are 26 hex digits (0..9, a..f), whereas WPA are 'proper' passwords. This might be a clue?
Macs are generally far more secure than any Windows machines (for several reasons), so the main danger to you I'd say is someone getting into your LAN by connecting to your router since there's no security. If they *can't* get onto your LAN, then (assuming your router is reasonable) then they can't affect your machines (unless the machines have opened ports to the Internet from themselves, such as some games etc. do), or you allow websites to install dodgy software etc.
If people do connect to your LAN, then if you have a strong password on the router, then the shouldn't be able to break your LAN, however you are then reliant on the strength of your computers (running Linux or Mac OS helps here). The best solution is multiple layers: Good Operating System (not Windows), don't run in an Admin account, run a firewall.
Personally, I run a mix of Macs, Linux & Even XP (with no anti-virus software at all) on my LAN, I broadcast my SSID (network address), using the old 128-bit WEP security (relative simply crackable if you really want to). I've never had trouble (and I've been using the internet since the early '90s), but then again, I know my neighbours (& having set some of their computers up for them, I know what they *don't* know.).