You don't really need to do either. You can just create a new profile yourself. It's really simple. I'm assuming you have the latest updates.
Create your own profile
All you need to do (if I remember correctly) is press the Xbox guide button to bring up the mini-dashboard, press x to either sign in or sign out (depending on if you are in the other person's profile). If in the other person's profile, sign out and then press x again to go into the sign-in screen. Scroll down until you find an option to make your own profile. If one doesn't exist, check the sides of the pop-up window to see if there is a specific button you can press to make a new profile. Then enter the name of the profile you want. It will either ask you if you want to make it Live compatible or it will just create your local profile. If it just creates a local profile, press the big Xbox Guide button in the middle to go to the mini-dashboard.
Delete Previous Profile
If you really want to, to delete the previous owner's profile, go to the "sign-in" screen like you've done previously and scroll to the profile name. One of the buttons around the pop-up should give a "delete option." Press the corresponding button and it'll be gone. You don't need to do this.
Get Xbox Live Silver or Gold
The following is if you want to join Xbox Live so you can download free demos, games, movies, add-on content, etc. This can all be done in Xbox Live Silver. If you want Gold, you can get your first month free for signing up (as long as the previous owner didn't use up all the freebies). Once you get to the mini-dashboard, select "Join Xbox Live." Then follow the on-screen instructions to become a part of Xbox Live. You may need to change your username to something that hasn't been taken yet. Everybody will see this name. Follow the instructions until the end and agree to join live for a month to get Xbox Live Gold free for a month. It'll convert to silver once the month is up. You can then get a Gold card at a store or buy one on your Xbox through a credit card to redeem Gold status. After doing that, just sign into your profile and all game progress you do will be saved. You won't be able to access any of the previous owner's gamesaves, so you'll need to make new ones. Essentially, it'll be as if you just bought it from a store. Thus, don't format the drive. This may cause the system to lose any updates it made so far (not sure). It'll also get rid of any demos and videos the previous owner downloaded. However, if you still want to, scroll to Settings on the main menu and search until you find an option to format the hard drive.
Warning: If you say you are under the age of 17 by putting in a birth date underneath that age, you won't be allowed to download M rated demos. I realize you're 29 years old, but wanted to give a warning in case anybody else in your family's younger and wants to make their own account.
Edit: I didn't realize how much I was writing. I added titles so you could read what you want, lol.
