Yeah, this hardware you have (Pearl made lugs) reveals that this could be any number of brands. Typically these are made in China or Taiwan. There are tens of thousands of these around, and are a very common beginner set.
Meanwhile, don't be discouraged by this at all. The ('secret') I like to try to share around is arguably the single most important factor of all. That is THE EDGES. How well they are cut, if they are even, if the edge is square ("True") and also what style of cut they have. Now, good heads make a huge difference (but they will be very limited in how good they can make a drum sound) if the edges are not done well. It is quite unpredictable to know if any one company/brand will have good edges. I bought a 1968 Slingerland and the edgework on it was awful. because of this, most pro drummers have a guy they go to for this stuff, even with their expensive drums.
Get your edges inspected and re-cut if needed.
Then, good heads will make it sound great. I recommend clear Remo Ambassadors for the tops and bottom of the toms. Wait, I see you already have some coated heads on there - they sound different than the clears, but these Remos are great quality heads. I would still try studio rings on them. (read on) I also recommend using "timbre pitching". While not original, this tuning approach was made wildly popular by DW in the 80s and 90s. Take the heads and hardware (as much as you can - some strip it down to the bare shell) and while hanging it on your finger, knock it with the other fist/knuckle. The shell will ring with its own pitch (note). Tune each head to this note and then use any number of muffling products (my favorite is studio rings) and they will sound fantastic!
BTW - doing all this may cost as much as $150 so think about this before you do all this - as this will make this quite an investment. Many drummers would not spend that much money on a kit of that level. Just know that it will be money well spent if you intend on keeping your kit for any number of years. Otherwise, just tune using this technique, use studio rings, and skip the edgework and new heads. If the edgework is good and the heads are not worn, this alone will still make a significant difference in the sound of your drums.
Best of Blessings with your kit!
John
