It would look a whole lot like Hong Kong, but with Houston, Texas lack of zoning restrictions, and a Silicon Valley number of start ups.
There would be a large number of toll roads.
Local streets would be maintained by private contractors selected local street maintenance assessment districts, or by groups of homeowners associations.
There would be more bank failures, since almost anyone could start a bank. (You would have to be 21 AND sober)
However, you could get a loan almost anything.
People would spread their business among multiple banks for safety, with no FDIC.
With little safety nets like Social Security, the savings rate would be much higher, providing more capital for business. Since taxes would be lower, the rewards for starting a business would tend to be higher.
There would be lots of different schools for everything.
Restaurant windows would be full of stickers from Zagat, Yelp and a dozen others rating the restaurants food, service and sanitation.
Wait, that happened, except for sanitation.
Police and the court system would still exist, and would enforce contracts.
Environmental damage would be punished by tort law. This would deter major pollution.
Licensing of experts would be competitive. A similar situation exist with Scuba divers, who get certified by NAUI or PADI
Some dangerous things would still be regulated, like airlines flying large jets.
Tort law dosen't provide a good remedy when a 737 lands on your house.
There are two ways to do the military – Switzerland/Finland/Israel/ Singapore model, where almost everyone is trained, and a smaller highly trained group.
The military would be pretty small, inexpensive, but very dangerous.
For example, they would have hidden long range missiles with biological weapons to deter attacks.