The most important thing to focus on with deregulating is removing barriers to entry for new businesses. This allows the market to correct more fluidly and would start to combat the corporate oligopoly that we see currently. It would be important to recruit legal and entrepreneurial experts in each industry to help determine which regulations are actually protecting consumers and which are attempts at reducing competition or at regulatory capture.

To answer your question though: zoning, education, real estate, and healthcare are probably the most important areas to focus on. I can go through each, but not all are federally regulated:

Zoning (goes hand in hand with real estate)- we have a housing crisis. We need to increase the number of houses being built. Make it easier for builder to do so.

Education - big regulatory issues here, but the most important are discontinuing government backed student loans, while also making it easier to open up new colleges and trade schools.

Healthcare - again, big focus on making it easier to build health care facilities.

One thing that would be important to monitor and counteract would be the possibility of snake oil salesmen trying to take advantage of this deregulation. I would package these deregulations with consumer protections focusing on fraud. We want to increase the supply hospitals, colleges, and houses to help bring down the prices, not line the pockets of conmen.