Good question, but budget could be a bit more well defined. In different price classes there will definitely be a wide variety of choices.
What I call a "inexpensive" speaker, my initial recommendation would probably be the Ascend CMT-340SE. In my listening they seemed to be well suited to rock, though they are even handed enough to handle everything. OK bass on their own, but will want a sub with them.
Budget speakers - Pioneer FS52s would be my default. Tweeter could be better, but bass is pretty decent and they don't complain when pushed hard. I run mine full range/no sub and have no real nits to pick with them for the price. To take those to the next level, the Affordable Accuracy upgraded versions of these by Dennis Murphy would be your next stop
The Infinity P163 bookshelf or P363 tower are not my favorite for everything, but I felt they did well with the sort of music mentioned. I listened to them with a lot of Porcupine Tree, Pink Floyd, and similar Prog. The 163s were not quite as good with vocals and fine detail as I would like, so for more subtle music, they probably wouldn't be my choice, but I also didn't expect a budget speaker to be perfect. I was able to push them to their limits where I actually achieved audible breakup with excessive levels when run full range. Crossing them to a sub will help with that.