Here's a checklist that I would use regardless of brand name.
1. Look at the other drum sizes and options. A 12/16/22 kit might be OK right now, but what if you want to expand or shift drum sizes. Do they offer a 24" or 20" bass? 8" or 18" toms? What else is on the menu for snares? Some mid-priced lines are kind of limited in order to save on production costs, so make sure you're OK with what you can get from them now and later.
2. Are they fairly well-built? Even the cheap kits are getting pretty good these days, so obvious goofs and flaws are unacceptable for a midrange kit. Die-cast clawhooks, memory locks, suspension mounts and wood bass drum hoops should be the norm for a mid range kit. Bubbled and warped wraps should be a thing of the past at this point.
3. Is the hardware flexible and comfortable? If you're gigging, you'll spend as much time twisting wingnuts and handling the drums as you will playing them. Mounting hardware should be strong enough to do the job, and simple enough to avoid a "chain of failure". Avoid gimmicks.
4. Will it work with other stuff I have, and if not, am I willing to make the switch to different hardware, pedals and stands. I have found that Tama and Pearl stand parts could be interchanged, as could Ludwig and DW, and Gibraltar made something that fit all of it.
5. Will the company still be around later? This is a little harder, since nobody can really predict what will happen to a specific brand, but the major players are still a safer bet than "Joe Blow's Super-Bitchen' Discount Drum Co."
6. How do they sound? How do they feel while making that sound? Am I having a nice time playing these drums? Do I want to risk my rent this month and buy the kit this instant? This one is subjective. The sound and feel is up to you, and not every shop can let you have a go at the drums. You have stated a basic idea with Chad Smith's BSSM sound, but getting that is more than just the kit. You have to dig up his methods and preferences for tuning, muffling, heads and so forth. It's in interviews and magazine articles. Happy hunting.
Beyond that, it becomes more a matter of your personal taste, and I can't help you with that. That's all you.
Stuff I don't worry about: Heads, stands, pedals or included cymbals. The heads seldom hang around for long, assuming I didn't just put my personal favorites on from the get-go. Stands are a nice bonus if they are well-built and functional, but pro-level stuff is pretty accessible, and I usually have that going before I get anywhere near new tubs. For me the DW 5000 was tip-top when I started buying my own drums in the mid-90s, and it came in around a hundred bucks, so no need to skimp on good pedals. Most included cymbals would be better off as hubcaps or barbecue lids, but you said you were OK in the cymbals department, so no worries.
I hope I'm helping.