Most of the cheaper computer speakers are designed for games rather than music, however people still buy the matching speakers for the Genos & Pa4x which suck big time, so the Logitech’s will probably do you fine if this is what you are after.
Active studio monitors are designed for sound accuracy so may be too revealing for your ears, but on the flip side most come with controls to modify them to your room and personal preference. (Best to pop down to a local music store and have a listen to a few)
No one can choose speakers for you as everybody hears things different, which is why it is vital to try before you buy.

Bill