What are the weakest components in my system?

would it sound much better with a better phono stage or cartridge

Methinks upgrading the H-K amp would do the trick better than changing phono, or cartridge...

Just tweak yr TT if you haven't, lots of info around.

I’ve asked it before in other posts and I’ll continue to ask it again; Are you using dedicated circuit breakers and some type of upgraded electrical outlets? If not and you are able to I’d start by upgrading your power (power filtration system). Should make a huge improvement by itself.

What aspect of your current system's reproduction seems most lacking to your ears at the moment? Do you plan to systematically improve all your components as finances allow? A bit of forethought can help missteps at the start of this process. I'd agree with Lak that good power is a great start in any system, but I'm not sure it's the best bang for the buck in your case. That would depend on how substandard your power is at the moment and whether your current system would reveal the benefits of cleaner power. It also depends on if the OP is a homeowner that's planning on staying put for while. The HK amp might be the first piece I'd look to replacing as well if you plan a systematic upgrade over time.

I am assuming the Harmon Kardon is an AV receiver based on the model # ... since your system seem to be dedicated to 2 ch listening, this would be the first thing I would replace. Maybe a vintage receiver/integrated with built-in phono stage

I agree with amplifier upgrade and like Jrinkerptdnet's mention of a Vintage solution. Sam Kim of Sam's Audio Labs is a master circuit designer and vintage equipment restorer/upgrader. Sam upgraded my McIntosh MR-71 to Triode and it's amazing. Check out this link to get an idea:

http://www.samsaudiolabs.com/about.html

I also like the dedicated circuit upgrade because I did that and it does make a difference but that can wait. Replace your HK and then do the AC. You will then be able to easily identify the weakest links after that.