I think your decisions as to what to do in setting up your "new" tank rests on what you mean by neglected. If it has aiptasia, hair algae, cyano, etc. I think you'll want to incorporate strategies in your husbandry to "manage" those problems in your new tank. These could include removing aiptasia and hair algae from rocks (many good suggestions for doing so - just search R2R); ensuring sufficient flow for addressing cyano; of course, maintaining appropriate water parameters long term, etc.
I would replace the sand if this is feasible.
And as RWG above says, don't rush the cycling of your new tank.
Good luck; if you post a picture or two, others can help you identify pest/neglect issues and offer treatments.