I haven't used KT66's but the I've seen people suggesting running them between 1.40 and 1.65. The preferred brand seemed to be the Gold Lions. A few things to be aware of - a lot of the alternative tubes are large enough that you can't use the tube cage, and some people have had issues with the tube bases not fitting and needing extenders - not sure if it is the amps that vary or the tubes, since for some people they fit fine.
The other thing to be aware of is that the newer SP8/3 has a base bias of .4 rather than the original SP3's 1.15, so depending on which model you have you may have to do a little bit of math to convert a suggested bias.
In general most people feel you get a better bang for the buck starting with the preamp tubes, rather than the power tubes. I ended up swapping out all of mine. For power tubes I've tried New Production Valve Art 350B's, NOS Philips 6BG6GA's with adapters, and NOS Russian Reflektor 6P3S-E's. Originally I was biasing these in my SP8/3 at around .5 or a little higher, but lately I've settled in on .45 with the Reflektor 6P3S-E's.
Also forum member 1BionicEar (Brady) is a great source for both tube info and actual tubes for the SP3. Here is my current configuration, and I'm really happy with it.
http://forums.av123.com/showthread.php?p=745228&highlight=Voskhod#post745228If you search the AV123 forum there are lots of threads that are hidden since they are no longer current with a ton of SP3 tube info.
Jim C