Hi Carliex
If you feel like dressing up, then go for it. You'll never feel out of place in a really posh dress at the races.
But equally you'll never feel out of place in smart casual either. Go as you please although its best to avoid really casual shorts and tshirt style.
Be sure to wear comfortable shoes though, there's a fair bit of wandering around and standing up to watch the races.
If its an evening meeting take a warm wrap or jacket and scarf as its quite cool after about 8pm on an open race course.
Be yourself, be comfortable and don't bet more than you can afford to lose!
Have a great time.