when you're done using the shop vac......HOURS later probably lol, some Murphy's Wood Oil soap will shine the stand right up, just don't use it on the TOP part.....you don't want any water/condensation building up on the wood from ABOVE the tank, then dripping chemicals into your water and kill your fish.
Make sure the oil soap stays on the stand and ONLY on the stand......and read the directions for best results. As far as the tops/lids/upper levels of wood I would probably start by scrubbing w/ some white vinegar to clean off calcium/water stains, and if you really want to put a shine on it, a little bit of vegetable oil (or canola/corn/olive oil is fine too), just make sure aall of your moving is over and done with because everything will be very slippery afterwards and you don't want to drop anything.
Take your time, no rush, be careful and get PLENTY of help when it comes to moving stuff so no one gets hurt and nothing gets damaged. Much easier and safer to lift 600 lbs with 6 people sharing the load than 3.