I would support legalization and regulation of prostitution like any other industry. I would not support government-run prostitution, and don't see a need for government-run liquor stores either.
And IMO regulations, if enacted, should focus on prostitute and customer protection, like disease screening, licensing, proper income, abuse protection, etc.
I can imagine in theory a prostitution business owned by prostitutes in sort of a guild structure, but realistically, I think corporate prostitution would be the norm, with owners/executives making all the money and prostitutes taking on the risk, doing the deed, and getting scraps and abuse.
Parts of Nevada already have legal prostitution. The prostitutes get hired as independent contractors that get to negotiate their own price but they don't receive any benefits. They have mandatory HIV testing and mandatory condom usage. A lot of them have really intense restrictions, like not being able to leave the brothel for long periods of time (if they want to keep their job, not like forcefully, or not legally anyway), or having to leave the county when they do take leaves from the brothel, or having curfews, or restrictions on driving, etc. Abuse by brothel owners and customers supposedly happens frequently, and many prostitutes have pimps even though they work at the brothels. So I don't know if that's any better or worse than illegal prostitution, although I suppose it can be a matter of what the specific regulations are and how strongly they are enforced. In practice I wouldn't exactly expect most other places to do it much better.