We sold our entire systems to a LFS. Definitely the best way to go if you want something clean, simple, and fast. Takes a certain amount of luck and good timing. You get better value if you go for credit vs cash. Consider doing this to get the equipment for your next build. It's a win-win situation if you've got stuff that they can use in their display tank, put in a maintenance account tank, or sell easily.
Next fastest is selling the system to an individual. You won't make as much, but it's fast and easy.
Selling it piece by piece is a lot more time consuming, but you are likely to make more money in the end, and it's cash. If you go this route, offer the colonies whole first, and break them up if you get a lot of people asking for frags vs colonies.
There's also the hybrid method - sell to individuals until you can't take it anymore, and take the rest to a LFS. Work this deal with them from the beginning so they can cherry pick the things they want the most, instead of just getting the stuff that doesn't sell.
Of course, you aren't shocked by any of the above, and you're calling me Captain Obvious right now.
Also obvious is to get your tank as healthy, spotlessly clean, and pest free as possible. The way your tank looks will make a huge difference in the amount of money people are willing to spend. I saw a LOT of dirty, unhealthy, poorly maintained tanks when I was shopping for corals. The condition of the tank had a direct effect on what I was willing to spend.
Whenever you sell to an individual, I strongly recommend dipping the corals you sell before they leave. It isn't a guarantee, but will definitely put people at ease.
