What kind of plant is this and what do I do with it , inside or outside

It is a croton.
Seeing that you are in Texas, I think it is ok to be outside as long as there is no frost. It is also an okay houseplant.

It likes to stay constantly oist.

I concur with the ID of Croton. I used to have 6 of these in the ground and can tell you with certainty they absolutely will not tolerate below 40º temps. Lost all 6 of mine in-ground because one night I went to bed forgotting to cover them with the buckets I usually used. Big mistake.

I also had two large ones in 21" pots for several years and moved them inside to sunny windows for winter after that.
This moving inside for Fall/Winter worked nicely for several years..........that is until last year's February freeze when both died. Sadly I had taken them down to our cabin property last Fall. What I didn't think about was that the cabin (not heated in winter) wasn't warm enough for them. I just didn't think of the interior of the cabin dropping below 40º since the walls are insulated somewhat. Another big mistake.

Failing their temperature sensitivity, I LOVE these colorful plants and plan to replace them this Spring when they are plentiful in the nurseries.

Yes, a variety of Codiaeum variegatum, commonly called "Croton", they are common landscape plants here in Florida. These are a few growing in my front yard.

Lin, your crotons are beautiful! you folks in Florida can plant anything outside and have it look stunning year round. I'm so envious. The Florida members here post photos that put the rest of ours to shame. How nice to have the perfect environment to make so many plant varieties happy.

Peggy, thank you. I've been in Florida 54 years now and I do love it but the older I get, the more the humidity really bothers me. We retired a bit farther south in the state about 5 years ago and we don't get as cold here so I can grow so many more things outside without worry of freezing temperatures.