1st Post, Welcome Aboard!

I would keep

Pioneer Receiver

Pioneer Speakers (level controls, yeah!)

sell Yamaha Speakers or use elsewhere or give away

New Cartridge with Headshell, Your tonearm has a removable Headshell, plan on moving the new cartridge to a better Turntable later so the improvement/investment is transferrable

My favorite not very expensive Moving Magnet Cartridge (works with your receiver’s phono input) is:

Audio Technica Headshell/Cartridge Combo Kit

VM540ML/H

includes a headshell (keep your old cartridge/headshell/factory aligned) for when you get a better turntable you can put the current one back on, sell old TT or use elsewhere or give away).

It has a MICROLINE Stylus shape, much better sound and lasts longer than others.

Adjust the level controls of those speakers for your listening space.

How old are your ears?

I cannot post links, but you can find and read this article

sound-smith dot com /articles/stylus-shape-information

Speakers often have the most impact on the system. Find something you love that works well in your room, and that can be driven by your amp.  Lots of great deals on used speakers in most markets. 

A cart upgrade is a never a bad idea! 😎

GIven the enjoyment you receive from your old and new LP’s, protect them and upgrade your cartridge and turntable. With budget considerations in mind, I would then look for a newer used integrated amplifier. Finally, you can upgrade your speakers. Not the order I normally do things but in your case it might make good sense.

You do not have to spend big bucks to put together a very musically satisfying system. Sort ought your priorities sound wise, do your research. When you ask for advice on this forum, you must be very specific as to exactly what you want a given piece of gear to do for you and at what price point. Otherwise, you will get a lot of random advice from members. Distinctly unproductive. (We all like to promote our favorite gear.) Good luck!

I am familiar with that vintage gear having sold many back in the day.
 

Currently the music room has a modern well reviewed but vintage looking NAD c3050 integrated amp available. That and chose your speakers there for a nice modern upgrade for less than $2k.  The vintage gear is neat but most good quality modern gear will slay it.  

@mapman +1! Plenty of used NAD integrated amps available on different sites: Audiogon, EBay, Reverb, USAudiomart ...