I'll ditto the other comment. There are so many out there looking to cross promote that you should have no problem finding a band whose sound you like. & That the band is looking for more notice.
Always get permission in writing. That way there is no confusion. It can be as simple as you & them writing a statement that the 'band' (owner of song rights) agrees to the use of its 'song name' in your 'video' for 'x' usage (or however you intend to use it) & spending the $3 (or whatever a notary costs in your area) to get a few copies of this statement notarized.
However, If you are looking to commercialize this in any way, I'd strongly recommend that you spend the few hundred on a lawyer to draw up more detailed papers to ensure rights & understanding.
Good Luck!!!
