The are great $200 headphones and mind-blowing ones for $1500, you'll have to set a budget so that people can recommend you the best options for that price.

My advice for now would be to rip your CD collection into flacs (or just download them if you can find them in that format, which you will for the most popular titles) so you can listen to them wherever and whenever you want from a PC or phone, having immediate access to every song without having to change the discs. Using a PC will also give you the possibility of equalizing your headphones, which is a huge plus.