You can do whatever you want for your own personal use. When you then go to publish your derivative products, you run into issues. Just use it for your own enjoyment, and leave it at that.
Performing in public, a song written by someone else, whether you copy their arrangement (i.e. play it note-for-note as they played it) or use your own arrangement, involves a performance royalty to the songwriter. This is typically owed/paid by the proprietor of the venue or the promoter. You, as a performer, may also be wearing one of those hats too. Your obligation would be to the performance rights society that the original artist lists their music: ASCAP, SESAC, BMI, etc.
If you sell recordings of your own version of someone else's song, you have wandered into something slightly different, a mechanical license. That is (in the USA) managed by the Harry Fox Agency, and there are statutory rates for what you need to pay, per copy manufactured.
Put very simply, none of this matters until that moment when money start changing hands. If you learned songs for 50 years, copying them down to paper for your own edification and enjoyment, but not disseminating those charts or selling recordings of your performances, you have no obligations. The moment you start making money... or somebody makes money, you wade into the copyright/licensing world.