A J1 visa is not an immigrant visa. If you apply for a J1 with intent to immigrate, and the USCIS figures that out, that can be deemed fraud. Also, if you're subject to the two year home residency requirement, marriage will not make that go away.

A K1 visa, technically, is also not an immigrant visa but it does authorize your entry for the purpose of marriage within 90 days of entry and your application for adjustment of status following marriage.

Best, in my opinion, to operate honestly and lawfully.

If you are out of status, you have to be careful about traveling. Even with a pending I-130 and I-485, you would want advance parole.