Is it illegal to meet someone from online, in person for the sole purpose of sexual conduct if it is at their home or my home?

Your biggest concern relates to the age of the person you are communicating with online. The crime that most commonly occurs is when an adult communicates with and plans to meet for sex with underage/minors. Should not be any problem for two mutually consenting adults to meet through online communications as long as their sexual contact is not involving illegal conduct...e.g. Drugs, crimes, non-consensual actions, etc. Having sex in public places raises concerns about potential indecent exposure charges. In most parts of the country it is still usually illegal under either local or state law to be visibly naked in public view. So you may be better to get a motel room even for brief encounters - many even have hourly rates.

You are on the edge, if the sexual services are being performed for any form of consideration it is illegal. Sex in a public place, including in a car, is prohibited. There are predictors, scams and entrapment on the web. I suggest you counsel with an attorney regarding this subject PRIOR to acting.