It is definitely a rough space, not designed for what we do.
We would prefer not to use an e-kit.
We are open to an enclosure as long as we can move it around. We are looking at moving it to the corner of the stage if we do so.
Audix D series mics
We have a budget for the enclosure and a pair of reasonably priced overheads.
X32 Compact, P16, and plenty of channels.
I have a drummer who says he knows how to tune a kit and I have no reason to doubt him, but I have no knowledge yet of what it takes.
Kit quality could probably be upgraded in due time. The cymbals are not good (I don't know what brand) and I don't know about the snare.
Our drummers easily play with a click, can play parts within reason and/or create their own. They tend to have a good feel and one of them is definitely more willing to play to the room than the other. Ongoing discussions...
Good to see that you have some nice mics, those will be a good starting point.
What type of kit do you have now?
Most kits can be made to sound decent, but having something better than not will be helpful.
If you are not already aware, used is absolutely fine for drums. There are lots of good brands, there are different tiers of kits to them. You may be able to find a great deal on an upper-tier kit that is a few years old, but not old enough to be "vintage." As long as the shells are intact (no cracks) and the hardware is working (not that it is hard to find or replace) then the most a drum should need the bearing edges sanded (if they are inconsistent) and some new heads. Honestly even brand new kits need the bearing edges sanded sometimes!
Note if you are willing to go for a kit that is not a current vogue color/design, you can probably find an amazing deal. For example, a little over a decade back custom drum shops got tons of orders for crazy colors, orange, neon green, etc. Heck, I even found a kit with Spam wrap (yes the canned meat!). Right now a natural look is the craze, although it would probably be something else soon.
A note on custom kits (smaller brands) they can be great, or not. The church I work at uses a particular custom brand that is built locally. They are nice sounding drums, but they are VERY difficult to tune; to the point, they can sound worse than certain other brands if someone is not diligent.
As far as brands go you should check out Yamaha. Are they the best kits out there? No. But they do make great drums, and used they can be affordable. If you wait on Reverb long enough you can probably find a nice deal on Absolute Custom or something similar.
I am not sure what type of music your church plays however a trick for you in making a drum enclosure work is actually using a slightly smaller kick drum. A 20" properly miced can be just as beefy sounding as a 22" can, and it allows the for the tom(s) to be lower.
For most music you will want 16" tom for a floor tom; however a 14" can be tuned fairly low; although you will probably need to replace the head a lot more with it being played tuned down that far.
As far as heads go batter heads (the side that gets hit) should be replaced fairly regularly, depending on how often the kit is played. I would recommend at least every 6 months, but some places do it every few weeks. It kind of depends on how much the drums are used and how much wear they exhibit. Resonant do not need to be replaced as often, I would recommend having something better than stock heads.
To the point of heads. consistency is really important. You will probably find that a certain tuning fits your needs best, this tuning will be affected by:
Genre
Iso-booth Acoustics
Mic choice and placement
Overall room
Note that some tuning choices and even cymbal choices don't feel good at the drummer's perspective, but feel great miced. This is a little counterintuitive, and for what it is worth is still expensive/quality gear.
I highly recommend that Youtube channel "Sounds Like a Drum" it is a very cool resource that I wish I had when I was playing. They really dive into lots of different ways to tune.
Once you find a head that works for your tuning I would recommend buying several. I know some churches that have a stack of 20 new snare heads awaiting deployment!
Personally, I am a big Aquarian fan. I love the sound of an Aquarian Super Kick II (batter) and one of their Regulator heads (resonant). It is a one-trick pony to how a kick should sound. About $80ish for their pair, but is worth it.
Also, check out a Zoro beater. They make a huge difference in the kick sound and yield lots of nice top end attack. They are about $30.
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At some point, I would recommend getting a nicer snare. A Mapex brass cat or black panther; or a Ludwig black beauty are common choices in my circles.
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Not sure what type of music your church plays, but if it is any of the more "modern" stuff. That is very focused on deep snare drums and very large dark sounding cymbals. Hats are often 15"-18" (usually made using crash cymbals) and 20" crashes and 22" rides. Expensive stuff as it usually hand-hammered. Remember that cymbals will crack, especially quickly with some drummers. Some churches find it is better to have drummers bring their own cymbals, others like the consistency of having a house set. Just realize they could be a yearly expense of $1500 if you have hard hitters.
As far as brands go Meinl, Zildjian, and Instanbul are common. Paiste sound fantastic, but anecdotally they crack quicker than most other brands).
Keep in mind that if a cymbal is hand-hammered that each cymbal will sound different and have a unique voicing. A good drum shop will have a whole wall of the good stuff. Even if a cymbal is a good brand and from an expensive series doesn't guarantee it is the one you want.
If you are on the hunt for inexpensive cymbals I have been quite impressed with the Instanbul XIST series for the money. For the price they are fantastic. If a local drum store carries them, have your drummer check them out.