Vinyl System Upgrade Path Recommendations

Hey gang! New to the forum but I’ve been really enjoying reading through old threads. I would be interested in the community’s thoughts on a natural upgrade path for my system.

Current System:

  • Pioneer PL-530 w/ Audio Technica AT 13 Ea
  • Apt Holman Preamplifier
  • Eico ST-70 (using as a power amp, line in)
  • Totem Arros

I listen to a wide variety of genres but with an emphasis on jazz and more recently classical. Overall the system performs well. I’m getting a good warmth for my taste and decent detail.

Moving forward I’d like to pull a little more clarity and separation out, but not create a clinical reproduction. I do dig the warmer sound. I’m also interested in trying to reduce background noise and pops/clicks. I’m already big on cleaning my LPs which has helped a ton, but I’m curious where to invest next.

I’ve also started listing more on headphones (Schiit Jotunheim + Hifiman HE400i) where I notice even more background noise.

So what do think? Better stylus / cartridge? Different TT? Alternative phono stage? Cables… ?

I try to be conservative with my spend (everything I own was purchased used), but I’m not afraid to shell out where appropriate.

Any suggestions? Thanks!

@stringreen - I've been really enjoying my Hifiman HE400i with Schiit Jotunheim amp. The sound is strong, acurate, and exciting. But I still enjoy listening to speakers a little more. 
You can only go so far with your equipment. A New cart will help tremendously. Playing clean records help.I was using Dishwasher brushes and fluid since 1973.I have always kept them clean .Now in poly bags .Years ago they said plastic on albums was no good it would shrink and warp your lps. There were times you bought a new record and it had pops and clicks. Which really sucked.I have never washed a record in the sink ,or bought a $1,000 cleaning machine.I had sold off my records and bought collections...One guys daughter sold off his collect I bought 300 lps in plastic covers in mint condition. She told me he played them once just to record them on cassette.Another Lady sold me her boyfriend's collection  60 lps all imports in mint for $300 but I had to have them....but I have been taken to bought collections at nite ,only to find them all and learn...i sold off1,500 and bought back like 800....I now have plenty to play....
Old thread but since limomangus decided to breathe some life into it I thought I would give an update on how my system has evolved in case anyone finds it useful. 

After lots and lots of component switching (amps, phonos, carts, speakers, cables) this is where I've ended up:
  • Pioneer PL-530 (The only piece that remains the same. I keep looking at upgraded tables but never pull the trigger. The Pioneer is so convenient and now that has an upgraded cart sound great.)
  • Denon DL-301ii 
  • Cinemag based SUT
  • Bottlehead Eros
  • Schiit Freya S
  • Decware Torii MKII
  • Klipsch Heresy III
I got very interested in tubes, SET in particular with high-efficiency speakers. I had another iteration of the system with loaded horn speakers and a Bottlehead Stereomour but ultimately decided I wanted more drivers. I've purchased nearly everything second hand or b-stock to reduce the overall spend. I can't say I'm done tinkering but this set up seems to be holding strong for now.