Sewing experts! I want to lengthen a T-Shirt by adding a faux layer. How would I do this?

I just bought a new shirt - unfortunately it was only available in small. It fits me fine except for being about 1-2 inches too short. I really like the shirt and want to make it long enough to wear. It's a black babydoll style T-Shirt (hence being way too short!) and I want to add a strip of fabric to the bottom hem and possibly the sleeves to make it look like one of those "faux" layered shirts. I am thinking either dark red/maroon or gray to be the color of the "layer" part. Would I just buy this as fabric from the fabric store, or would it be easier to buy a thrift store shirt in this color that already has the bottom hemline and then just cut off the bottom and sleeve ends to use as the layers? Also, I know virtually nothing about sewing. Is there some sort of iron-on type of material that could be used for a project like this? Thanks in advance for any help/tips!