I guess I'll need to take it to the dealership and have new key cylinders & keys put in..?
This is where it gets a little convoluted.... since we both have '99 Limited it should be the same for you as it was for me.
There are a few key possibilities split between physical cuts and what the car immobilizer sees. The 2 physical keys are normal (operates everything) and Valet (doesn't work in the glovebox). Doesn't matter if you have either of those, though if you have no reason to lock the glovebox from someone else with a key, I'd just get the dealer to cut you the Physical key from your VIN (or key code, if you have that).
That brings us to the digital side, the immobilizer. There are 2 keys here too, a Master and a Sub. These are strictly related to being able to program a new key or not (well, and work within Techstream, the dealer software, some functions need a Master key). You can identify those by what happens to the Security light just to the right of your rear window up/down switch. If the light goes out immediately when you put in a key, you have a Master. If it blinks another 2~3 times, you have a sub. With a Master key, you can erase all keys and program new again, thus deleting all old keys from the system. Someone with an old key could gain physical access, but the key will never start the vehicle.
This is where you get to decide your personal level of risk. Are you okay with someone being able to enter the vehicle? Then just have the keys programmed to remove the one that's missing. You *MUST* have a Master key to do this though. No Master key and you're looking at over a grand for the Dealer to get you a new key, ANY new key and somewhere in the $300~400 range for an independent locksmith to do the same (well, there's another option, cloning, that can be done for about $100 but that won't erase the one that's stolen).
If you're not okay with someone gaining easy access and just breaking a window instead, then yes, you'll want the tumblers re-keyed. I'd have an independent locksmith do that job though, just going to be cheaper and better to have someone who puts food on their table by working on locks, and Only locks, do the job rather than a line mechanic who does locks occasionally.
There are some DIY options in there too... if you're cheap, handy or just plain interested you can go the Techstream route for doing your own key programming (assuming a Master key) for about $20 and ethics that allow you to use software you didn't pay for. If you don't have a Master key, there is a way you can DIY a fix for that (I had to learn this myself, involves programming an EEPROM chip and some soldering), I think I had about $40 into that solution. And re-pinning locks is something common enough that there are thousands of youtube videos on it.
Forgot to say that I still don't know what Alarm you're referring to. The key fob is just a keyless entry, locking and unlocking doors, rolling down the rear window. That's all it does. And there's an Immobilizer system that disables the fuel pump (or ignition, I didn't dig that far) to keep the engine from starting when the key isn't recognized. I don't think there's anything else to it though, but I'm frequently wrong and still learning this vehicle.
