By far, the most important choice is the right amp for the particular speaker. The sound of the system will be primarily determined by the amp-speaker matchup. If you want to hear what tubes can do for the sound, start with the proper tube amp for your system. Tube amps vary greatly in sound, much more so than do good solid state amps.
While I am a tube amp fan, I find that there are many that do not suit my taste such that I would take most solid state amps over such tube amps. I generally don't like most high-powered tube amps that use a lot of tubes in parallel pushpull to achieve very high power; most sound hard and brittle to me and I would be more likely to take a solid state amp.
Fortunately for you, you have speakers that will work with fairly low-powered tube amps. You will have to audition some to get a feel of what amps you like. I have my own preferences which are for some single-ended triode (SET) amps and pushpull amps running EL 84, 6L6, or KT 66 tubes. The EL 84 tube is run in a lot of more reasonably priced amps and it delivers a lively sound. SET amps that I like tend to be quite low in power, which may be an issue even with your high efficiency Cornwalls if you have a large room and like to play music at very high volume. Also, although SET amps appear to be very simple, so they should be affordable, they demand a very good output transformer so decent sounding ones are NOT cheap. You should at least audition a good SET amp, but, they might be a bit of a risk when it comes to compatibility.