Should speakers be upgraded before preamp and amplifiers?

I can recommend the Rogue Pharoah hybrid integrated amp to easily and effectively meet your goals.

What do you want from your system? What is missing right now? You have new speakers and vintage electronics. Do you want to stay with vintage?

Room sounding ok? Otherwise this is where you get the biggest difference.

You seem to be a vinyl person. Depending on cartridge, I would consider a dedicated phono-stage and see where that gets you. Maybe also vinyl cleaning equipment (vacuum and/or ultrasonic). my 2c. 

Should speakers be upgraded before preamp and amplifiers?

Like everything else audio, that depends upon who you ask and/or who answers.

I did a quick search on those speakers and they seem pretty decent.  They might benefit from better electronics in front of them.