Do you want to make a good first impression without being formal? Then go casual dress. You may substitute jeans for something like khakis. Non-flashy dress shoes or good quality regular shoes will work. Just make sure if you wear sneakers or somethng they aren't dirty and that they don't have holes.
Unless she is a psychotic bitch(like every other girl in your topics) she will probably like it, and be impressed. If you go out with her more or become serious, you can dress down a bit. For he first couple times suggest going up though.
As said before, make sure your hygiene is in top shape. Combed hair(make sure it doesn't frizz out when dry), shower, deodorant, brushed teeth, trimmed nails, shave.