The most important part of the skinny jean is the material. Lots are cotton and spandex, which will give you the tightest fit. Some are even cotton and lycra. The best (budget) pair I’ve bought so far are from Forever 21, they’re a cotton/polyblend/spandex blend.
Here’s the drawback (did you think there wouldn’t be any for $13 jeans?) First off, they bleed blue when you first buy them. It took me a few hours to realize my hands were turning purple from my jeans! But, just wash them with all dark colors a few times and they’re good to go. Also, they wear out easily. I think that’s to be expected with something so cheap, but at that price you can always replace them!