Before I write the following, keep in mind that this is in legal terms and not necessarily practical.
As soon as you sample a song, you are breaking the law. This doesn't mean that people don't do it, but legally, you're not supposed to use any part of a recording for your work unless you have clearance. Of course, how do you know you can sell it before you even make it? You probably can't, so most major releases have samples cleared once they have plans to actually use a song. In general, if you're not selling a lot of units, no one that matters will know that you're using their work without permission.
When you sell something, make it clear that the samples are not cleared and that you are not liable for clearance. Even better, get it in writing. If you tell someone that a sample is cleared and they go on and they get a cease and desist order, you're probably going to be liable for the expenses.
... or you can just use music that had been released before Copyright Act of 1976 and is not protected by law, if you want to be sure.
This is incorrect. Many older releases are copyrighted and protected by copyright. With major recordings, if the label didn't retain ownership, then there is an artist or writer/composer/etc... that owns the rights to the recording or other aspects of the production. If the person has passed, copyright can be renewed by the estate, and that's often what happens. Not that there aren't obscure recordings out there that have expired copyrights but it's not the case for just about all popular music.