SEEKING ADVICE: Which component would you upgrade first?

people are not paying attention

either to OP's budget (+/- a few hundo)

or his existing speakers, I looked them up

go to hifishark, check the prices asked for his Pioneer HPM-100 Speakers 

what the hell do you think would be better for a few hundro????

these speakers have Level Controls, giving the ability to adjust for both the space and OP's preference.

The receiver/tt/speakers certainly would reveal the improvement of a new cartridge, AND, the investment of a new cartridge can be moved to a new TT when ready.

Save money for quite a while before looking for better speakers

My suggestion is to start with cleaning up your power. Once you do that everything down stream will take on a life! However you will need more than a few hundred to do it right.

The HPM-100's were designed by an engineer Pioneer hired from JBL and were their answer to the 1970.s JBL L-100. Nice speaker in its day but IMNSHO, the absurd prices those speakers are bringing today is tied to the vintage-gear rage. Speaker design technology and philosophy have progressed greatly since the HPM-100's were built. A wise hi-fi mentor once told me, "if you want to make the biggest change in the sound of your system, get different speakers." I agree witih him. And if it were my decision, I'd sell the HPM-100's and take the money from them and look into some Vandersteens, Monitor Audio or Sonus Faber.

Within your budget ...

If you're keeping those speakers, you should check for dry rot on the surrounds of the drivers. Fixing those could be the best money you spend. I would also look at how you have your speakers installed: location/posittion, on stands, how they are coupled to the stands or floor - these improvements can make a big difference without costing much aside from your time and patience to dial them in.

After that, new cartridge for turntable (and good installation!) and outboard phono stage. Good options for both from Rega, Denon, and others. 

After that, cleaning all your connections and replacing cheap patch cables and lamp cord wire with decent wire from Belden, Blue Jeans or others. Easy to spend a fortune on wire, but I do find basic sold brands can make a really nice improvement over old "free" stuff that came with the gear.

A streamer could open up your system to the world of digital, and so could a blutetooth receiver or cheap cable that connects your phone to an open input.

My rule is work your way in from the outside. Sources first. My priorities are:

1. speakers - source for your ears. The single largest improvement you can make to a system is to choose the best speakers for your ears, your room, your music and to match the rest of your gear.

2. Front end sources: Analog: cartridge, tonearm, phono stage, turntable (in that order, IMO). Digital: DAC, source (streamer, computer, device)

3. Preamp.

4. Amp

5. Everything else: cables and tweaks