I wouldn't use Magic Wand. If you insist, then I'd suggest you adjust the tolerance level down so it doesn't grab more than you want. Mine has a tolerance defaulted to 32 - I would lower it to 6-8 to start. But I would recommend you use more accurate selection tool instead.
Here are the steps I would follow:
Duplicate your layer
Everything I do will be non-destructive, but it's handy to have a copy of your original for the later steps.
Make the best selection possible
First step is to make a decent selection. I would try Select > Color Range. Lasso or Magic Wand are going to do ok on the legs and body, but will be terrible on things like hair.
I've used a low value for "fuzziness" and "range" in order to not let Photoshop select more than I want. I chose "Sampled Colors" although you could try Highlights if the background is light enough. Select the "additive" dropper and click away on all the background until it is all highlighted. Adjust the fuzziness and range to get as much background without selecting too much of your subject.
Next I would use refine edge to get the edges and hair as good as possible.
You'll end up with something like this. Close but not near perfect.
Save as a mask
Now click OK. This will load the selection. On your duplicate layer, click on the create mask icon. The mask will have your subject mostly black and background white. Probably the opposite of what you want, so invert the mask (Ctrl/Cmd-I or Image > Invert).
Edit the mask
You should have some pure white (subject) and pure black (background). You will have two problems though. You'll have some grey parts that are neither black nor white. And you will have parts of your subject, like the shoes, that are similar to the background and are black.
To address the grey areas, just choose the mask itself, then use Image > Adjustments > Levels and push the sliders towards each other to increase constrast. That will make some of the light grey turn white.
Now take a white brush and fill in any remaining grey areas in your subject, and correct anything like the shoes that is masked out. Use a black brush to fix any background areas.
By using the mask, you will work non-destructively and can correct things.
You should end up with a mask something like this:
One tip is to insert a blank layer that is close the the background you want to use in your final composite. For example I chose red. That way you can pick up things that might stick out in the final.
The below took 5 minutes. I didn't use refine edge, so the hair is rough, but the rest is a pretty good extraction I think