Well, who’d a thunk it!?!  First off, WELCOME cblystone1!  And thank you for asking this question!!! 

I love turnips, they are MAGIC in stews and whenever possible I get some to put in the stew or soup pot.  I put a few large chunks in early in the cooking, then remove those after they’ve cooked to mush (it’s a texture thing but they really add a ZING to the stew or soups!).  Then when I add the carrots and potatoes, I add cubes of turnips as well.

I also like them mashed either alone or with potatoes, but I’ve never tried to pickle them!

So far in my searching, I’ve found several recipes that include either beet juice, or some par-cooked beets to turn them pink.  Not sure I care about that.

Otherwise I’ve seen them with a mixture of equal parts water and white vinegar, just a little salt, (about 1 Tbsp per cup of the water/vinegar mixture) Heated then poured over the sliced turnips and processed.

As far as additional ingredients, here are some other extras.

2 or 3 slivers of garlic per jar

1 or 2 sprigs of celery leaves per jar  (never heard of that but most of those are a middle eastern recipe, sounds interesting!)

Or, chopped celery (same as above)

Jalapeño slices (or other hot peppers, amounts vary to taste)

Another recipe used turmeric (1/2 t per 8 cups of liquid) in the water/vinegar which colored them a very bright yellow, that was a very interesting thing to me, I’d have to try that one on at least part of the jars I think.

That same recipe also included

1 cup sugar (again per 8 cups combined liquid)
1 teaspoon coriander seed
1 teaspoon mustard seed
1 teaspoon black peppercorns

Now, I’m not giving any one recipe that I found since I don’t have any experience with any of them and we can all do a google search on “Pickled Turnips” but since I wasn’t enthralled with any one of them either, I’d be tempted to try a batch or two of a simple mixture of with the water/vinegar/salt liquid and garlic with a bit of the celery.  THEN I’d have to try some of those with the turmeric, that sounds better than beet red (or pink) to me.  I 'might' try a small batch with a few slices of jalapeño, or maybe one whole jalapeño per jar, since I like some zing.

Mostly they all called for the turnips to be sliced about ¼ inch thick, some thicker, I’m wondering about slicing them like French fries?  …though all said to slice them across the grain, they can be stringy after all so maybe put them in the French fryer sideways? 

OK, I've either confused the heck out of people or gave some interesting ideas.  Smack me if I need it!