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
I started with a Project Debut a few years ago. One Scout and thousands of dollars latter dedicated to the analog side, on it’s best day it sounds as good as a cd depending on the record. Most new repressing sound like crap.
When I was starting out with a high end system back in the 1981, I purchased the Dynavector 10X3, an Ultracraft tone-arm and a VPI 19 (since upgraded to a IV version and used for 78 rpm records).  Sure, my current turntable/arm/cartridge system is $16K, but the old system is still very musical.  I suggest looking for a good condition, used high end table, same for arm and a matching cartridge for that arm (compliance-wise).  A Denon 103 makes an inexpensive but great sounding cartridge to start with on a good used tonearm (or maybe a Rega 3 if compliance is correct).   You should spend about $1000 total to get a set-up to at least meet the CD quality sound and in some ways better it.  Analog is just more cumbersome than digital.  I love both, mostly based on mastering of the recording.   Look for a higher end used deck or stick with the Project. 

Get a better cartridge for sure.  I've used that deck for 2 friends who inherited their father's large record collections but didn't want to spend much on turntable/arms.  After using my recommendations for a better cartridge, they thanked me for the great sound at a bargain price (one got the Ortofon mm Blue, the other a Dynavector 10X5)
Yes, the IC is rather poor quality.  A good used one should run you under $100.  My SME IV also came with a piece of crap IC for what was once a $3500 arm.
Update from OP here:

Long story short: bought a Clearaudio Concept from my local dealer. He gave me a good deal I could not pass up. Just the standard tone arm and standard “concept” cartridge.

Just set it up with my dealer’s help, and it sounds great. No comparison with the Project Debut Carbon DC Esprit which is going back.

To complicate things, I have an Ortofon 2M Bronze coming in the mail, so question becomes: is the Ortofon Bronze better than the standard Concept cartridge, or should I just return it ?