Best thing to do if you're not going to donate it is, pull out the hard drive and drill holes in it! About 1/4 inch holes and no one will get anything from it. If you're going to donate it, just wipe everything off from it and it would take an experienced person to get anything from it.
I have been told that you can not completely erase info from a hard drive. Whenever I get rid of an old computer I always take the hard drive out before discarding it. It has been recommended to me to that I smash the hard drive with a hammer before throwing it away. So far I have not done this, I just keep the hard drive so I can access it later. Congrats on the new computer