As with any task to designate a "best," a best 845 tube doesn't exist. First, it depends on your amp. One of the touted advantages of tube amps is the ability to "roll" or change tubes from one brand or build variant to another. Now, I say this as a lifelong tube audio devotee: if tube changes alter the sound of an amplifier, then which produces the accurate or highest fidelity sound? It becomes quite subjective. In some respects, audiophiles use tubes, like cables, as fixed parametric tone controls to tune the sound of their systems to personal preferences.
For example, nearly all of today's 845 amps ship with the cheap and ubiquitous Shuguang 845A commodity tube. It's super cheap and reasonably tough, and sounds fine out of the box. But I've not heard a single 845 amp that sounds its best with this tube, no matter how many times the maker says "the best tube is the one we ship with the amp." For most amps, the Shuguang 845B will improve everything over the 845A, at a modest increase in cost. The B tube will prove long-lasting and both electrically and physically durable, able to handle amplifier circuits that run the 845 aggressively.
But the Shuguang 845C has some interesting qualities. Its transparency, high frequency extension and transient speed are remarkable, though it produces about 20% less power than the A or B tube. It also is rated for less plate dissipation than normal spec (~75w v. ~100w in the A and B tubes) so in many amps it will have a short life and run borderline runaway, but that's a separate matter. Point is, in an amp like my Audion Black Shadow monoblocks, the 845C sounds shrill to the point of unusability unless paired with a speaker with a rolled-off top end. But if used in a Tri amp, which is voiced more like Shindo for a too-soft top end, and undynamic with rounded transient character, it *can* be an asset, depending on your preferences.
For most, the 845B is the "best" 845, because it is neutral, toneful and delivers good bass control, plus it's affordable, reliable and predictable. Some people prefer the Psvane 845-T to the Shuguang B tube, but the sonic advantage is not large and the newer T shows indications of being less reliable. It certainly hasn't established the long-term track record for reliability yet. But it's worth a try for someone restless.
The standard TJ tube has lower-than-spec plate dissipation, so it isn't universally compatible. The TJ Carbon plate that Sophia sells claims full RCA spec, so it should be fine. I haven't heard it. Nor have I yet heard Canada Fuller, Create and Synergy.
The KR 845 is the outlier. It is an interesting design innovated by Kron and it's off spec. It's dynamic, transparent, vivid. The initial version had serious reliability problems due to the ribbon filament shorting. This has allegedly been corrected though I can't personally vouch for current reliability. The maker of my amps, Audion's owner, says it's a drop-in replacement with no problems and it's his favorite way to listen to the amp. Prices are nearly at NOS levels in the US. In some other amps, some modification to the filament supply may be needed.
What's the best 845 tube? Tell me your amp, your speakers, your room characteristics, your tolerance for risk and expense, and your general sound preferences, and we can narrow that down to a "most likely to be best" for you.
Phil