I had a cutting with a rose on it in a vase, after the rose died, i took off the dead part of the stem and left the stem and two leaflets in the vase.. within a week it sprouted so I decided to try to grow the new plant! This was all improvised and unexpected, but so far it's grown a good inch and a half from the top of the stem.

So here is where I need help!:

I don't have access to rooting hormone or perlite. Some potting soil from the plants in our kitchen seems to have some perlite in it so i used that soil (see picture below). Does this look good?:

I wounded the stem around the bottom all the way around (see below), but later i read that it should just be on two sides. You can see approximately how big the stem is in my hand. What should I do to make sure this plant will grow!? It was picked from a garden rose bush at my friend's house. It began growing just sitting in water. I dropped some soil into the water for nutrients, after it grew some more, I put it into light soil in a cup. The cup doesnt have holes for water to fall through the bottom so i made sure the soil was just moist. After a few days I carefully took the dirt out with the cutting to check if roots were sprouting. They weren't and the bottom was turning brown so i cut off a little bit and wounded the stem all the way around. Here I am with the stem in a fresh cup of soil. What should I do now?! I want it to live a grow into a beautiful plant!

How moist should the sirt be?
Here's the moisture level from the meter:

Check out the following pictures to get an idea of what I'm working with:

You can see the discoloration/browning at the tip of the plant.

I'll appreciate your help so much, thanks!