Trace/outline a section and color?

The pen tool is likely your best option if you need vector using AI. But if you don't need a vector image, then Photoshop would be better.

I don't think you need to use Image Trace if what you want is to show an area over a map you have.

First I'd start by making the outline shape on a new layer. In the layer panel, click the Create New Layer button on the bottom (2nd from the right).

Then make your outline shape. You can do that with several different tools. The pen tool can be tricky for new users, but if you don't need specific curves, you could just click at every corner you need to make. If it's a more organic shape, you could use the blob brush. You might just try experimenting with the various drawing tools to see which feels most comfortable.

Once you create your shape, select it, and in Illustrator CC 2018, you can go to the Properties panel to reduce the opacity and/or click on the word Opacity and select a blend mode from the drop down menu.

BTW, good job giving it a try in Illustrator and for posting your question. Everyone starts somewhere.

what does the png look like? there are lots of options in image trace, so it's possible you just haven't played around enough with it. keep the options window open (window > image trace)

otherwise if it's simple enough, make a new layer above the placed png and draw the outlines with the pen etc.