1) Very neutral, clean and articulate. Provides the most detail, air and extensionThis school of sound would be my normal preference

Siemens early long-plate 5814A. Since these are pretty mucy unobtanium, Raythen 5814A (probably same as CBS 5814A) are also quite neutral and detailed/clean.
If even these are too much $, I can recommend Sylvania 6189 or Tungsram 12AU7 to try. Often can be found cheap and in the neutral, clean school of sound and can "hit the spot" in many situations.
Regular Siemens ECC82 tubes are in this school of sound but not quite with much magic.
RCA Cleartops are either hit or miss, but if they work in a component, they can sound very clean.
2) Warmer side of neutral but still good detailAmperex 7316 PQ
Valvo 6067. Ahh, if I could find some more...
Radiotechnique 6189 not exactly "warm" as in bass quantity, but sweet tonal warmth
Early long plate RCA 12AU7A's very solid sonic signature and texturing. Can hit the spot in certain systems but can veer into "maybe too warm" and darkish if mismatched. My favorite of the RCA's are the almost black-plate like carbonized-plate ones.
3) Lots of body, very warm (maybe too warm)Some of the Mullards fit the bill. I like Mullard CV4003 better than the costlier Mullard M8136, which seems a bit more "stuffy" sounding to me. CV4003 is lush but not exactly solid-body type of density; for that, the early RCA long plates are the way to go.
4) Lifeless, stay away from.Some of the much-later date tubes, including Raytheon 5814 late-production or Philips 5814A, etc.