What would happen if a person was out in space? would they get picked up by the pull of gravity from inbetween our planets, or sun? I'm curious, if someone were to be floating out in space. Would they eventually be captured by the gravitational pull from another planet or sun. To be more specific the person isn't anywhere near said planet or sun they are just passing between them. My question, is there some sort of current in between planets or sun that can have the slightest effect on an object passing through?
There are no currents.

It all depends on the initial speed of the object, and the distance to the sun and planets.

If it's moving pretty slowly initially, it will eventually get captured in a loop orbit around some planet or maybe around the sun.

If it's moving pretty fast initially, it will described a trajectory through the system and eventually leave, never to return.

This is no different from what happens to asteroids, comets, the planets themselves, etc. This is all the play of gravity. This is called orbital mechanics. It's part of what is popularly known as "rocket science".

There is an app called Universe Sandbox. Install it on your computer and play with some solar system simulations. Setup a simulation with a central star, and just one body near it. Launch the body with various speeds. See what happens. The various scenarios unfolding from there are the answer to your question.