Alright, I'll give you a primer.
First of all, if possible you should try to get an Xbox with a motherboard revision below 1.6. Why? Because on motherboards below 1.6 you can solder a few wires and do what's called a "TSOP Flash." This allows you to flash a custom bios to the onboard chip, and will basically give you most of the advantages that an actual modchip would. Normally hard drives have to be locked with a unique key for the Xbox motherboard to work with them. If your hard drive dies and you haven't done a TSOP Flash, and you don't have a modchip, and you haven't made a backup of your Xbox's EEPROM, your Xbox is a brick.
Now, what
@tech3475 is referring to about the capacitor is the clock capacitor. This capacitor normally allows your Xbox to keep track of the time while it's unplugged, but they used crappy capacitors that are prone to leaking acid, which will eat away at your motherboard and will eventually brick your console if you don't pull it off. They fixed it with a better capacitor on the 1.6 motherboard, but for any older motherboards it will have to be pulled. It's really easy to do, really only takes about 10 minutes. You can get more information from here:
https://www.reddit.com/r/originalxbox/wiki/clock_capacitor
If you have everything you need to do the 007 Agents Under Fire exploit, then go ahead and do that, but there's another way of modding the Xbox using a "hard drive swap." Basically, you need a desktop computer with an IDE interface (some people have had luck using a USB adapter on a laptop with a Virtual Machine, but I personally haven't tried.) You download, set up, and burn a CD called "XboxHDM." Then put the cd in your computer and boot off of it, at the main screen hit the Pause key so it doesn't continue booting. Then you start the Xbox, wait a few seconds for it to unlock the hard drive so you can access it, and WHILE IT'S STILL RUNNING remove the IDE cable from the hard drive and hook it to your PC. This allows you to access the drive and softmod it without needing any specific games or needing to prepare a memory card with an exploit on it. There is a risk of damaging your console or PC from moving the IDE cable while everything is running, but I've modded at least 10 Xbox consoles this way and have never had a problem.
Did you buy a bigger hard drive to throw in the Xbox? If not, you can still softmod it, but you'll want to burn your games to disc. The stock hard drive only really has enough space for one or two games depending on the size of the games.
If you did, most of the replacement Xbox Dashboards (XBMC, Evolution-X, UnleashX) all come with built-in FTP servers. You can use any FTP client (I recommend FileZilla) and drag and drop the game files onto the Xbox. Considering a lot of Xbox DVD drives have been known to die, this is the preferable way of playing your games.
--------------------- MERGED ---------------------------
Yes, the Xbox won't play burned DVD games without being softmodded first.