Brand new to vinyl: Help!


I am brand new to vinyl, but quite established in digital (CDs, lossless streaming, etc.).

I made the first foray to vinyl by purchasing an entry level turntable - Pro-Ject Debut Carbon DC Esprit.

I am using an Ayre pre-amp with phono stage and also Ayre amp.

While I am happy I have it up and running, I don’t think it sounds as good as my digital setup (Directstream DAC).

So what can I do to improve, short of buying a much more expensive turntable?

Things in my mind:

1 - Since it accepts DC power, buy a linear power supply

2 - Since my Phone stage on my preamp only accepts XLR three-pin connector, I bought a male RCA to male XLR cable from Amazon, less than $20. Do I need a better interconnect?

3 - Upgrade the cartridge (it comes with Ortfofon Red something)

Thanks!
128x128thyname
Yes, enjoy and I haven't seen a cartridge yet (or speaker) that didn't improve some when broken in.  
Any recommendations for a record cleaning machine? I bought one of those brush cleaners from Amazon, but I think I need a more robust one. Thanks
thyname, A bit of icing is missing from your cake if you are trying to convert the single-ended output of your turntable into balanced mode for your Ayre.  The Ayre phono section will sound best when fed with a true balanced signal. This is not so arcane as it sounds, because all cartridges are inherently balanced devices.  To achieve a single-ended signal from a cartridge, typically the "ground" pin of the cartridge is connected to the shield of a single-ended cable, along with the turntable/tonearm ground connection.  Your hard-wired IC is probably configured this way. A typical single-ended phono stage works fine this way. 

In contrast, a balanced signal consists of two halves, one "plus" and one "minus".  To get the most out of that output with respect to feeding the Ayre, you would want each half of that balanced signal from the cartridge to be carried on a separate conductor where the two conductors are identical.  The typical XLR on a balanced IC carries the plus half on pin2, the minus half on pin3, and the grounds (turntable, tonearm, etc) separately on pin1. Thus, for carrying the phono signal in balanced mode, you want to connect the "ground" pin of the cartridge (which by convention is really the minus half of the signal) to pin3 of an XLR, keeping it separate from TT/tonearm ground (which goes to pin1) and carrying it on its own conductor. The Ayre sounds best this way. (I used to own an Ayre phono stage; I tried it both ways.)  The hard-wired single ended IC on your new TT kind of makes for a problem in achieving that goal.  (There's nothing "wrong" with it, because most phono stages are SE circuits.  You happen to own a rare true balanced phono section.) But meantime, find out if you enjoy vinyl using your new set-up as is, which does sound like a big improvement over the original.  What I am talking about here is, like I said, icing on the cake if you want to go the last mile.  With a little surgery best performed by a knowledgeable tech, you could make the change to optimize the balanced connection, if you perceive you will be moving forward with vinyl.
Thank you very much @lewm !

Definitely something I plan to do down the road, if I am lucky enough to find someone that understands what you wrote and knows what to do
thyname,

lewm is dead on. Big improvement in sound quality using a true balanced wiring harness from your cartridge pins to the K-1xe’s phono input. Don’t put it off. I can help you if you PM me.

Dave