If you continue using ICS at least enable the WindowsXP firewall on the server.
Even though you may be exceeding 10 users, you can probably continue using your XP box (assuming it's running XP Pro). The 10 user limit generally doesn't apply when doing simple peer-to-peer file sharing and most users usually aren't using a network share all the time.
Server 2003 is a lot easier to setup (and a lot more secure out of the box) than Server 2000, but I don't know if you want to go to the expense if you've already paid for Server 2000. First time you boot 2003 you get a wizard that asks you what tasks the server will perform and only enables the features you're using (sounds like the only one you'll enable is file sharing).
If you bought a regular DSL/Cable Router (they are all NAT routers) at Office Depot, you would connect the DSL modem to it and then the router would connect to the hub/switch. If everyone is setup to obtain IP and DNS automatically you're good to go (you'll probably have to force everyone to re-aquire an IP address when you install the router, or just reboot all the computers).
With a NAT router yes, you could shut down the server for maintenance and no one would lose Internet access. Yes you could lose the 2nd NIC on the server too.
You want to proceed slowly. Network administration is a whole new level. On the other hand it sounds like you have the basics under your belt and this could be a great learning experience. Nothing like hands on.
Something else I should mention is data backup. What are you doing for backups? You should be backing up your data (just your data) daily on tape or (preferably) DVD media.
For a small business I recommend using CD or DVD media (DVDs are so cheap now you might as well). You can store nearly 9Gb on a DVD standard in compressed format and nearly 18Gb on a dual layer DVD (although dual layer media is still rather pricey). For most small businesses, 9Gb is plenty. DVD is a cheaper solution than tape, and unless you're backing up monstrous amounts of data, more convenient. DVD also lets you do archives which is more problematic with tape.
I like to use Stomp's Backup MyPC software. This app DOES NOT run on a server OS however, so you need to install it, and your DVD burner, on one of the workstations, and backup the shared folders from there. Another good app that does run on a server OS is NTI's BackupNow!
What I recommend is use a rewritable DVD for Monday thru Thursday. Then Fridays use a DVD+R to make a permanent archive backup, and file that backup away. You'll have an archived backup for each week. WHY? Because if you do only daily re-writable backups, you can easily find yourself in a situation where your oldest backup is only a week old, but you realize someone deleted an important file a month ago.
Remember to TEST your backups regularly - actually run a restore operation on a backup disc once in a while (don't need to recover all the data, just several test files) and restore them to a separate folder (don't overwrite any actual files you're using) just to make sure you can read the backup. Also you should check your backup log every day to make sure it worked, and there were no errors. Remember that is anyone leaves a shared file open on their workstation, the backup will skip that file because it can't backup files that are in use.
As noted earlier I said to only backup DATA daily. There is absolutely no reason to backup the entire hard drive. What you should do is make a Norton Ghost image backup your server's hard drive. It's a good idea to do this anytime any major changes are made to the server. In a disaster scenario, you can restore the hard drive from the Ghost image (so instead of spending all day re-installing Windows, drivers, and setting up all the user accounts and shared, your OS can be restored in just a 30 minutes or so. Then you can restore your latest data backup. Viola! You're up and running again in 1 hour instead of 1 day or more.
Also while you're setting up your server, if it doesn't have a RAID 1 Mirror hardware right now, you might want to consider it. Don't bother with a software mirror - use a disk controller that supports RAID 1 (if you bought a server box from Dell or some other OEM vendor it probably has onboard RAID otherwise you can buy a RAID controller card).
You want to set this up now - it's difficult to change an existing OS to a RAID setup.