Depends how loud you want to go with the clean tones. Under normal circumstances you would expect to get around 20W out of a pair of 6V6s. At the higher voltages (around 440V), we can squeeze a bit more power out of the 6V6s, as well as get those signature Hiwatt tones. The amp starts to break up at around half way on the MV control, without the Overdrive stage engaged.
Opinions and tastes regarding tube brands will vary. The JJs are a little bright to my ears at these voltages, and I suspect Tung Sols may help reduce that brightness. However, Lawrence likes the amp amp with the JJ 6V6s and then runs it all the time on the Bright input.

Recently I've also been testing a pair of Russian 6pi6 tubes (one Sovtek and one Brimar!) in the amp and the tone totally kills, with plenty of crisp edge, while without being over-bright. With the Overdrive stage engaged, I honestly think I'm hearing some of the best rock tones I've had out of any amp. It's just been a blast to play it.

And I'd always been a total Marshall guy before this amp....
BTW I was just reading Watford Valves' 6V6 shootout from 2005, including both current production and NOS tubes. They say that they first burn-in tested all of the 6V6s at 500V, before doing the tone shoot out. So it seems that most currently available 6V6s should work happily in the Triwatt.
But if you really want lots of loud clean headroom, then KT66s are the way to go.