I would like to sell a computer, but don't know what to look for when using a utility to clean previously deleted space. Someone told me ONLY to use the Gutmann algorithm, but I really know nothing about any of the other methods.

I really don't want to spend a ton of money either since it's probably not something I'll use for quite some time aside from now....so as inexpensive as possible would be good.

Anyone have any suggestions?

Hello and welcome to BC.
Using the Gutman is like dropping a nuclear bomb on an ant hill. It work but why? I preform a wipe on every clean install, except for new drives. The utility I prefer is Digtal Dolly, but Active@KillDisk-Drive Wipe Utility will do the same job. KillDisk only does a "Quick Wipe" While DD has a full suite of utilities.
The Gutman wipe makes 38 overwrites, while the Quick wipe makes only one overwrite.
KillDisk is a freeware that provide a Quick wipe solution.

Hope this helps.

You can use, and fortunately it is absolutely free, Eraser to overwrite unused sections of your hard drive. You can elect to use the Gotmann alogorithm, and it will overwrite the empty space with it 35 times (this can be a lengthy process, so Eraser has other and faster options that might suffice). You can download Eraser from:

Eraser

Regards,
John

yep, aint that the truth...
I use Eraser for my "once a month whether it needs it or not"
cleaning with 3 passes followed by a defrag.
If I was giving it away I would use DBaN and the 7 pass DoD method
to wipe the entire drive.(of course you would need to reinstall your OS then)