Is prostitution a state or Federal law?
will I avoid a setup if I call a provider from New York to NJ into my house, which state agency would cross State lines anyway?

Ordinarily prostitution is a state crime.  In your hypo, New Jersey law would apply because that is where the crime would have taken place.  New York law doesn't apply to actions taken entirely within New Jersey.  The fact that the lady happened to be in Ney York when you called her only comes into play if she solicits you during the call, but even then she would be the one breaking NY law and not you.

Crossing a state line wouldn't make any difference if we reverse the hypo and imagine you traveling from NY to NJ to see the lady.  If you get caught the police will give you a citation and a court date, and if you don't appear the court will issue a warrant for your arrest.  NYPD can then ask the NJ authorities to execute the warrant and hand you over to them. I don't know how likely it is that they would do this for such a minor case, but requests like this are routine and they are routinely granted.  A more likely alternative would be for the NY police to just sit back and wait until you are pulled over for a traffic violation or otherwise come to the attention of police.  Officers routinely check for outstanding warrants against their detainees, and warrants for failure to appear never expire.

Thank you
let me clerify my question,
if I call a girl on the from NY and say I am here in Howard Johnson I would like your company she says ok its 300 for my company I say ok,
she comes from NY,
she meets me in my room, I put down the envelope pants comes off without a word about money or sex
at what point did the crime take place?
Can assume she is not an NYPD officer since no crime was done in NY and NYPD is busy enough not to look for trouble in NJ

The crime is comitted once you and she begin having sexual contact.  The elements of prostitution do not include saying anything.

btw, you would probably have to pay a hefty surcharge to get a lady from NYC to go to NJ to see you.  I don't think $300 would do it.

It is against Federal law to transport a woman across state lines to have intercourse. The Mann Act can and has been used to prosecute prostitution across state lines.

Please clerify what your saying.
I can transport my wife to a different state to have intercourse.
I can probably call a woman from a neighboring state to Nevada to Fuck her for Money as long as the offer is not made in a state where its illegal.
what kind of law are you talking about is it the transport or the offer or the call when those it become federal?

It's my understanding that the Mann act covers 'crossing jurisdiction with the intent to commit an act that would be a violation in the originating region'

Taking a 16 year old girl to RI from MA to have sex and avoid MA's age of consent statutes is illegal due to this act.

Technically, Going to Vegas to gamble is a violation of this act too.

And even going to Thailand to have sex with 13 year olds is a violation of this act.