New to Turntable - what're involved in playing LP?

There's a lot of very good entry level decks that come with pre-mounted cartridges. They're about as plug and play as it gets. Speak to the seller and get a sense of what you'll need spec-wise from a phono preamp.

After you amass LPs and decide you want more out of your setup, get familiar with cartridge installation. A local dealer is invaluable in this regard.

That's how I started out anyway. I bought a Pro-Ject 1Xpression deck which had a pre-mounted Sumiko Oyster cartridge, and an NAD PP2 phono stage. I upgraded to a better integrated that also had a great internal phono stage (Bryston B60). After moving, I found a local Rega dealer who's a vinyl guy. I bought a Dynavector 10x5 cartridge from him, and he installed it while explaining everything to me. When the time comes to replace it, I'll buy something from him and ask him to watch me install it. He's a great guy in this regard and would be happy to help me out.

One thing I'd strongly suggest is good cleaning stuff - for your records and stylus. They don't need to be expensive however. I bought some Mofi record cleaning fluid, a wet brush, and a carbon fiber brush from Music Direct. Nothing fancy or exotic.

After you amass a decent sized collection, a vacuum cleaning machine works wonders. I bought the KAB USA unit for about $150 or so? Took my vinyl sound quality up several notches. I also added using a hand held steam cleaner that I already had (it was about $25), and that combined with the vacuuming took it up another few notches.

It's easy to get caught up in the cleaning stuf and other vinyl tweaks. One thing at a time IMO, and don't get overwhelmed by it all. It's not as difficult as it seems.

Cleaning is an essential process. No matter how good your equipment is, it'll sound like crap if your records are dirty. That doesn't mean it has to be an intricate process though.

RO817
There are several reasons that I would discourage you against vinyl.
At the top the number one reason which made the compact disk an instant World Wide success was it's over whelming convenience of use.
My suggestions would be to put your money into improving what you have now be it mods to your player and or vibration control including finding the right amps for your Harbeth speakers as you mention, I think money well spent.

Someone like yourself in this position of never owning a record player, a collection of Lps and everything that should go along with it including developing your own expectations with vinyl playback.
You could very easily find yourself not enjoying it and throwing money at it is not a solution either, it takes time and gained knowledge.
Sorry for the wet blanket , just something to think about carefully.

Get a "plug and play" model so you dont have to spend much time with set-up. Rega, Sota and VPI very nice TTs, with used ones as an option. Then I would seek out quality used vinyl at your local record store or EBay and Agon are good too.

Or am I jumping too far ahead because I may need to upgrade my digital source (CD or SACD player) first and find the amps for my Harbeth?

Since all of your experience is with digital, it may be better to get that setup first, since you are familiar with the format.

Doing both together can be a headache. Analog has less dynamics, but other nice things going for it. Even someone that is a veteran with both, may have a hard time starting with new gear using both formats.

I got back into it after having been all digital for the last 20 years and I am having a blast with it. It is certainly more work than digital but the sonics are simply splendid; more life like than sacd / cd. As others have suggested buy something plug & play or buy from a dealer who will set the table up for you if you don't want to do it yourself.