Removing the shelves is a smart move. I suggest taking the glass doors off too, just to prevent any breakage during the move.
If you're hiring movers, clearly label these items as fragile and let them know which parts are delicate. It?s a good idea to transport the glass parts yourself if you can.
I came across a resource that might be useful for estimating moving costs:
https://threemovers.com/movers-charl...columbia-cost/. It provides an idea of what to expect when hiring movers, even though it's about a specific route. This might help you prepare financially for the move.