difference between 12AT7. 12AU7 and 12AX7 Tubes

That's right: all 3 tubes are what is called a "dual triode". They all have very high gain & practically the same pin outs. I didn't know that they could be used inter-changeably but then your preamp manuf. might have designed this in.
I think that the 12AX7 might the least microphonic whereas the 12AU7 & 12AT7 are more. My integrated JoLida uses 12AT7 drivers the JJ 12AT7 is quite microphonic. I also think that 12AU7 is also noisier than its peers. I know that my CAT pre Mk1 version used to have 12AU7 but the design now has 6922, which are much quieter.

Sovtek makes a very good 12AX7 called the 12AX7LPS which similar to the Siemens long plate version that was/is considered one of the best 12AX7 ever made. Very popular tube & lots of choices.
FWIW.

Here is The Tubestore.com 'choosing pre-amp tubes by gain factor'

The difference is the gain where a 12ax7 = 100, a 5751 is 70 and so on. I often recommend for instance that if you want more headroom choose a 5751 as a replacement for a 12ax7 with a black plate triple mica being some the smoothest and warmest tone. Guitar players who have distortion pedals can substitue a 12au7 due to its lower gain and it makes the overdrive much more usable. If you look online you should be able to find a chart of the difference in gain for all of these family of tubes. Joshua