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
First you can replace that awful cartridge to something much better. Even if you will upgrade with turntable and tonearm later you will need a cartridge. Everything starts with a cartridge when you play vinyl. I have upgraded the same turntable for a friend, we just changed the cartridge and he was so happy. His new cartridge was Stanton 881s mkII with Stereohedron stylus, but it could be much better with Audio-Technica AT-ML170 from the 80s (this cartridge is one of the best MM money can buy) and works fine on many tonearms. It's a mid compliance cartridge. You can also try wonderful Grace F9 or F14 cartridges. 
@tablejockey  you are 100% right on expectations - and I am totally aware of it. But I am not investing big dollars on a top shelf TT until I figure out vinyl is good for me.

Phono stage is top class. It is a Ayre K-1xe preamp with the optional phone stage included, which at that time costed MSRP of $1,800 additional upgrade.

I was just thinking in terms of temporary "stop gap" measure doing something with what I have.

Thanks!
Find a dealer/store who sells hi-end tables and see if you can get a loaner to try in your system. That would include a nice cartridge. That should help you to make up your mind. If you don't care for the sound then no sense in upgrading your Project, and you can simply sell it. Or, maybe the dealer will have a future sale.
Kenny
thyname-perhaps someone will chime in with a suggestion for a  value cart.  I imagine you want minimal investment moving forward. I'm not sure that would be the solution, since the stock cart is supposed to be decent,relative to the table.

You bought a budget table, it comes with limited expectations.

 Audio Technica seems to be a go to,recommendations sure to come.

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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