this gets asked every other week
the basic answer takes two paths:
1) do what you want no-one is going to sue you unless you're making money; which is essentially a variation on it is easier to ask for forgiveness than it is to ask for permission (more on that in a moment)
2) clear everything to avoid future damage to financial and personal health, what I call the "it is easier (and cheaper) to ask for permission than it is to ask for forgiveness" method of business (more on that in a moment)
I advocate the second path
I do this because otherwise you may end up paying a huge price down the road top get the permissions you want to continue to be a success.
A simple clearance doesn't take long to do and can be handled by a clearing house, licensing group for the most part. the costs may seem exorbitant to beginners but are a true reflection of the music's true value to the owners of the recording or publishing rights.
Even if you reinterpret (interpolate) an existing track to circumvent the inability to obtain a license to use the recording, you may still be liable to license a use of the song it is associated with, depending on how iconic/recognisable the backing track is: this type of license however is simply a cover license, similar to what you do to release a song written by someone else on your own album/ep/whatever
on the forgiveness vs permission front
forgiveness assumes that the owners of the rights are willing to allow you to continue to make money from using their intellectual property. History does not support this position; most cases show that the owners may refuse permission or take partial or complete ownership of the recordings you have made and still insist on damages, actual and punitive
obtaining permission up front insulates you from such grab and run tactics and ensures that your revenue stream is legitimate