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

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.

Unless you already have a record collection I would advise against it. Of course you can always find cheap records at Goodwill if you like Lawrence Welk, Andy Williams and Herb Alpert.