Ok, I realize this is a broad question, so I will give more detail.
Right now I have a set where different drums are from different companies, basically. I bought an entry-level set and sold 2 of my toms and bought a different one, my snare's a different company, and my stands are just whatever I could find at a good deal that isn't complete crap. So I'm looking for uniformity, in part.
I've personally played on brand-name sets: Yamaha, Pearl, Slingerland, Tama
but I know that heads can essentially alter the "true" sound of the drums so I don't know that I can really go by that. I feel like I would need the same heads on the same-size drums on different brand-name sets to see what differences the drums give while playing them, but that's where I'm asking this question. What is it about your favorite company of drums that you like in their drumsets?
And I was talking to someone about this a little bit ago, I've been to websites of musical instrument dealers and they have listings for "Beginner" sets, "Intermediate" sets, and "Professional" sets. I don't really know what to look for. I don't know how much different the intermediate set would be from the professional set, for instance. I'd like to not by another "beginner" set, so I want a decent one, but I don't know all of the companies and which sets are lower-end and which are higher-end and why. I could research specs but I still wouldn't have them in front of me to play on. So this is opinion based, I realized, but I want to know why you do or don't like certain sets, certain types of wood shells, etc.