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
thyname - you are up to the task, if you read paragraph 2 from @effischer:
The simplest solution is a Mobile Fidelity device called a Geo Disc; about $50 from anywhere.  It isn't the most accurate but should be sufficient for what you want to do.  It's a single point protractor with arm pivot point reference and precision molded spindle hole.  It's a fast, easy way to double-check a pre-existing alignment.
@thyname, I think the first thing that has to be done in order to get meaningful advice is to quantify the problem. How bad is the sound relative to what you are used to? If a LP sounds vastly inferior than a digital representation of the same master tape, then something is wrong with your set up that needs to be addressed before you even begin to consider upgrades.If the differences are more subtle, on the order of what your digital reproduction sounds like now vs how it sounded before some meaningful upgrade, then you can get your turntable set up by an expert at an audio shop for around $150 to make sure you're getting what  you should be. They can also check your RCA to XLR cable to make sure it is designed as it should be. Not all XLR connections are equal; but that a long story. 
If you should need a new cable, this is one you can customize for length that is quite good and a very good value.

https://store.wireworldcable.com/collections/interconnects/products/oasis-7-audio-interconnect-cable?variant=979670263
Best of luck!
Jim
If you can spend that much money down the road- save for the 4k-use a good chunk of it for a cartridge. I went from a $600 shelter to a Lyra Kleos and wow! You might have enough left over for a decent upgrade to a used turntable with arm from reputable(look at their history) sellers. Make a fair offer, don't lowball and save even more money.

Look at cartridges available on audiogon. You can see a lot of great deals on cartridges from reputable sellers either demos or only with a few hours on them up to 50%off. And read a lot about them, their qualities and what you think will appeal to you. Analytical, warm, etc...Many private sellers have a fair bit of money and get bored quickly. Thank god for that.

Then get a good clean original copy of Graceland and go to town. Great vinyl is full body visceral in an exciting way.
@stringreen  @johnmarzy @2channel8 and @vindanpar : thank you very much.

I will get the Geodisc.

Getting a new cartridge is so difficult for people like me who are not familiar with their brands, etc. A lot of research to do.

Anyone here from DC area?
@2channel8: would this be designed as it should be (XLR male to RCA male and preserve the balanced signal for the Ayre k-1xe)?

http://silversonic.com/products/interconnects/bl-1/