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.