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
FWIW, If not sure go the least expensive avenue, Vynil gets real expensive real fast. Sure all the recommendations are great and useful but you'lL never recoup your outlays if you decide you don't like the whole Vynil experience.  It can be quite a shock not being able to hit a button to skip a track. There is a lot of intimacy required with vynil. Just my opinion. I personally am on the vynil side of the tracks.

I took note of all suggestions. Before I go any further:

Is it worth tweaking my current turntable (Pro-Ject Debut Carbon Esprit), or saving up money to buy a "good" turntable down the road?

I am thinking I should be able to save about $2,000 to $4,000 for a good turntable in about six months.
Thyname

Looks like plenty of info and suggestions to confuse, and possibly waste money.

A favorite album and cartridge in your budget should give you an idea if records are for you.

All the reviews are favorable for the humble Project, when kept in context.

No cable,mat etc will elevate a table meant simply for enjoying records.