I'm currently in a situation where I'm considering looking for open land/property, putting a used travel trailer/RV on it and living there as a main residence for the time being.

I make enough money to finance a house no problem but my credit history isn't good enough. Not really excited about the idea but its where I'm at in life right now.

I'm not sure what the laws are surrounding this, as far as whether its legal to do this or if restrictions are county by county. Have any of you done this before? If so what is the process of getting approvals, hookups for an RV/Travel trailer, etc?

There likely are areas where you could do this, but where we live it was expressly forbidden in the deed restrictions in our somewhat rural multi-acreage lot development.
Maybe find a real estate agent that specializes in open land, and find out what your options are?

Real Estate Agents are like used car salesmen.

The local township or city office is who you need to speak to.

My township has all the zoning laws online.

Like above, when you find a piece of land you're considering call the township clerk and ask about it.