At one point in my life I moved 11 times in 11 years and have moved a couple more times since then: local, cross-country, international.
Locally, I’d usually just use those “student mover” or “2 guys with a truck” types.
For LD, the best I ever used was Paul Arpin. They really took the extra care.
Of course a lot depends more on the crew than the company, which is why pizza and soda and the promise/hint of $20/guy at the end of the day for “beer money” (or whatever) seems to go a long was as well.
If you’re paying for this move yourself, I’ve found the most economical way to go is to pack the non-breakables yourself (“PBO” = packed by owner), and have the movers pack the breakables. (They’re not responsible for breakage if you pack it). Then they move everything for you.