First, I am a staunch believer in Garbage in equals Garbage out. Great speakers are great at reproducing garbage if your source, preamplifier OR amp are not up to the task of not mangling the signal.
My experience is modest speakers sound better with higher end electronics than higher end speakers with modest electronics.
At you budget you should be able to get some good gear that will make your speakers shine. I would upgrade the speakers last.
Tube pre-amps are tricky, as they can easily mangle the signal. The more you can spend on the pre the better. I have had several and was unaware of how much better a good tube pre sounds or how you get what you pay for in terms of sound quality. I have had a Decware it was very nice and tubey sounding but a little noisy but enjoyable to listen to. I had a Schitt and did not like the sound at all ( and I rolled a lot of tubes with it). I am on my 3rd Allnic and I think they make a great starting point although they have gotten pricey even the older used units.
A big part of the "garbage in" is the electronic noise in the system which is not distortion. I have spend a lot more on Conditioners and grounding and noise absorbers than I have on my speakers and every time I add something for the RFI EMI ground plane noise or such my speakers sound better so it is like a speaker upgrade.
I think the Sansui has to go. :(
