I got a Hardwired Tiny Terror (only 2 Preamp and 2 poweramp tubes), so I can share a bit of experience.
As I have tried a handfull of different tubes in different combinations and there are a lot of differences. Just for reference, my cab is a Marshall 2061x, which is a england made 2x12" with Celestion G12H30 speakers.
For powertubes I have not tried as many as I quickly stuck with "Tube Amp Doctor EL84 str", short the TAD EL84str. Now that change was done a while, but I will try to recall the changes. They certainly got me one thing: More balls! Made that little amp sound bigger for sure. Generally they are a little different than most EL84s. Some people claim they have some 6v6 flavour to them, but I canīt comment on that. To me it seems like they have more low and high end than the stock and a crunchier midrange. Also gave me more punch. Rocking tubes for sure, really like em.
Generally they delivered more beef and power, at least in feel.
I still wanne try some good old fashioned NOS Mullards as they are often said to almost be the gold standard for tubes (certainly love the one I have in my tube mic), but those are hard to come by and afford.
On the preamp I again tried some things more recently.
I always felt that JJ 12AX7 tubes were rather on the warm side, which I now use in my amp since I can freely mix preamp tubes as they donīt have to be matched I really tried several combinations. The actual combination I now use is a JJ in V1 to give me that warm, roaring, yet somewhat smooth base sound and then a Tung-Sol in V2 if I recall correctly as that is generally I very nice tube I found, organic, 3D sound (yeah that shitety term xD), but also rather trebly and to agressively bright for me in V1, so I use it to add sparkel and dimension to the JJ sound. Now I get what I feel is a very harmonically rich sound, which is roading but balanced, with great Orange character put for a little spin.
After all the V1 is the most critical one as it does most the lifting.
I tried both 12AX7 and AT7s in both V1 and V2. My conclusion was that the AT7s drop the gain too much for my use, which distortion only with this amp, gain @ 2 oīclock plus a Klon(e).
Different preamps are really your main concern here I feel as they really shape your tone, especially the V1.
Since you donīt seem to be using the amp for distortion you might concider using 1 or 2 AT7 tubes. Find one with a bit on the warmer side for V1, possibly a JJ would be nice if their AT7s are like their AX7s. That way you reduce the gain from the amp making it easier to get clean tones. Follow with something for a little sparkle, maybe something like a Tung Sol AX7 in V2. Then fill up with maybe JJs as they are good and not that high in price or 2 different brands again.
In the end chances are that you will try around a bit to find the combination and order of tubes that works best for you.
The JJ AT7 in V1 followed by a AX7 might be a good starting point though. Depending on how you get your tubes you could just get a JJ AT7 and Tung Sol AX7 first and try those in different positions to get an idea, then buy 2 more tubes, try different things again and really do this step by step as I did.
You could even just start with one tube no problem and walk that through V1-4. Although the phase inverter stage, which should be V4 should work best with AT7s if I recall.
When the actual amp experts chime in you will get an even better idea.