Should speakers be upgraded before preamp and amplifiers?

Absolutely speakers first. Find some you really like the sound of at resellers and friends.  Notice what they’re paired with at careful listening can shape your component decisions also. One of the things to recall about speakers is that bookshellf speakers with stands take up about as much room as floor standers. Bass reproduction desires could steer you towards floor standers too.

@infinid00 Just sent your link to four people..So thanks. In the words of someone. "It's the room!" 

That’s quite a time capsule you have. I had the same receiver with a PL-19 with JBL 100’s in 1978. That being said, ans mentioned above find the speakers you like and then choose an amp that compliments them. At your price point I would consider a new Technics TT and a Bluesound streamer. If you buy an integrated amp and speakers used you would be able to assemble a better sounding system. Later you could get a separate phono stage and upgrade to a better DAC. You can spin your vinyl and stream internet radio without buying a music subscription. But you need to visit stores or a trade show to find what you like.  Happy hunting , Mike. 

Everyone is full of advice on how to spend your money.  Forget that advice.  Start with an assessment of what you currently have.  What do you like about it?  What are the positive things about it that you want to retain in your new system?  What do you hear that you would like to improve upon?  What music sources are you most interested in?  Vinyl?  CDs?  Streaming? etc.  Once you have a clear idea of what you want to achieve, your shopping list will be easier to start to sort out.  Be flexible.  You might start out thinking that you want a tube preamp, but discover that you can achieve your objectives with a class D integrated, and if you do something like that you can afford much better speakers.  I say this because in my primary system the electronics are all top of the line Conrad-Johnson tube, whereas I just assembled a new system for my second home and bought a Marantz P10 on close out for a song that sounds quite good even in comparison.  I did not start out thinking I would end up with this amp, but by knowing what my goals were for the sound sought that is how it worked out.  Do a lot of soul searching.  Start with listening very carefully to what you have now.  Remember, what do you like, what do you want to improve?  I spent 6 months getting inside my own head on that stuff first.

Thanks for the good advice and recommendations, looking into them.