Jason,
Machine levelling is a very debatable thing, some saying it does no good, others saying, if you don't do it, you aren't getting the best from your lathe.
I am from the second school of thought. The first school are usually the ones who have no engineering background to begin with and are most probably lucky in they get some semblance of accuracy with their lathe.
When you actually come to level a lathe, you soon find that all lathes bend, some like a banana, a few very little, but they all do bend and flex. Basically, the heavier and more massive the main castings, the less it will bend and twist.
The more rigid a frame you mount it on, the better for the lathe not to go out of shape.
In the early days, they would recommend a stand from say 4" lumber with a 2" thick wooden top.
Nowadays, the 4" lumber for the legs is reasonable in price, but the 2" top would need a second mortgage, and after a time it would most probably warp, as modern wood is not like the old outdoor seasoned timber.
My personal suggestion to you would be as you suggest. Modern worktops are very stable as long as you have a good frame under it, plus you have the advantage of the wipe and stay clean surface, a big advantage where you can have oils and coolants splashing about. I have used it throughout my shop.
This is Bandit, my joiner, who integrated the 4" x 2" frame into the secret room in my concrete bunker.

Uncle Bogs, testing out the strength of the kitchen worktops he used on the wooden frame. If it can take my weight leaning on it, your little lathe will be a piece of cake.

A wooden stand, by the time you have purchased everything, won't be much cheaper than a dedicated machine stand. But in your situation, it would be a great advantage, as you can have one full length of worktop, with the lathe on one part and the rest for all your other stuff. Also, if you integrate it into your shed frame, you will find both structures will stiffen up a lot.
John