A work in the public domain can be used freely without asking permission and/or paying any kind of remuneration to rights holders (with respect to the moral rights in the countries where they are protected by the law).
The possibilities of using, modifying, processing, remixing, and doing a mashup of works in the public domain are endless.
Suppose you intend to use not only the work but also a particular phonographic recording of the work. In that case, it will be necessary to verify that the related rights are also no longer protected.
Some websites where you can find Creative Commons-licensed vocal tracks for your music bases are www.looperman.com, http://ccmixter.org, and https://wordpress.org/openverse.
Works released under a Creative Commons license can be freely used without asking permission from the rights holder, without prejudice to the terms of the license applied. Many of the acapella are released under a CC NC-Noncommercial license, so you should contact the rights holder if you want to make commercial use of them (for the explanation of CC licenses, see FAQ n. 20).
When content is in the public domain (i.e., no longer protected by copyright) it can be shared with the CC0 tool.
Anyone who intends to legally DJing in public must have lawful access to the works they perform, either because they purchased them, or because they are the rights holder of them as a phonographic producer or, finally, because he/she has received the rights directly from the rights holder (music downloaded illegally from Youtube or other platforms that allow downloading does not fall under this definition).
In some countries, if in your DJing activity, you need to perform in public music reproduced from CDs, LPs or original digital files, the copies thus obtained do not fall under the definition of “private copy” but under “working copy”. As such, it must be authorised by the rights holders, and therefore by the collecting society which issues a specific DJ technical copies license (See aldo FAQ 22).
In order to legally perform DJ's activity, you must comply with the tax and social security rules to which you are subject and which may vary from country to country.