You must also not shower her with too many gifts and compliments too, especially if you're not in a relationship and you just met her. Giving her fun is enough, and if you really want to gift her, at least make her work a little for it (like asking her help you find something on a shopping trip). Otherwise you can be the next nice guy she might take advantage of. (once again, in a relationship it's a different case)
Need-based gifts like scaffs, coats and sweaters are often the best gifts for someone you just started dating. This will show that you care and are interested in getting to know her more. Getting tickets to an event is also a great gift.
When you first start, we recommend giving something little - don't set the bar too high. Little gifts related to an inside joke, souvenirs from business trips, etc - we have a post w/ some other tips: http://bit.ly/17bnJ3K