Brand new to vinyl: Help!

I find it helps to think in terms of %'s.  With a decent cartridge (think $400-$500 new) your table, arm, interconnects, etc., can get you 90-95% of what is reasonably achievable.  It is that last 5-10% that requires super stable table, seriously engineered arm, and a cartridge and interconnects made from un-obtainium.  Try a mid-compliance cartridge and let your speakers tell you the truth.
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BTW: If you haven't yet, make sure your table is dead nuts level, best tweak ever!

@tablejockey  when you say "value cart", did you mean "cartridge"?

How do I know which cartridge is compatible with my turntable?

@thyname,

I own a Pro-Ject Debut Carbon Esprit SB. Here is what I did to improve the stock performance, at a moderate price:

Replaced the stock interconnect cable with a cable from Audio Sensibility. Significant improvement IMHO. I paid the $10 extra for break-in service so I didn't have to wait days/weeks.....

Performed a complete re-alignment, including level, overhang, azmuth and tracking force. VTA was checked and was OK, but not easily adjustable.

Replaced the Ortofon 2M Red Stylus with a 2M Blue Stylus. When I did this, the cartridge moved in the headshell and I performed a complete re-alignment again.

I like to sound I'm getting at this price point.

+1 reubent.  FWIW, I'd start with the 2M Blue stylus and complete re-alignment.  Those things often have a bigger effect than cables.  I'm not a big fan of XLR adapters; just another mechanical interface set to introduce noise.  Caig DeOxit should be all you might conceivably need given the age of your gear.

Cartridge compatibility is not a concern; your Ayre will handle pretty much anything.  Just make sure your phono section gain is set to 40 dB and resistance is 50 kOhms for your 2M Red or any other MM cart.

That said, some speakers like some cartridges better than others.  That's something that is largely subjective and has been addressed in many other threads.  Again, I wouldn't worry about it; you;re just trying to get a handle on whether the vinyl thing is good for YOU.

Note that the LP itself can have a dramatic effect.  Some are just plain bad, and some will rock your world.  Most are in the middle somewhere.  Use a decent cleaning process (once more, lots of threads here on that) and pick some music you like.

FWIW, I feel that vinyl is superior to digital in every way.  I have a superior DAC, disc player and vinyl rig and after doing hours of A-B testing, I'm always happier with the vinyl.  It just sounds more natural to my ears.

That's why this is such a fun hobby:  Finding that happy listening!