Go to the Varrock clothes shop near the General Store. Change your clothes to make you look rich. I suggest changing your clothes to this:
Legs: Fine breeches, breeches and princely breeches are the most finest and royal looking. Royal blue looks very good with these pants.
Arms: Princely sleeves and fine cuffs look the best.
Torso: Woolen vest, princely vest and fine shirt look the best. The best color choices are forest green, burgundy and sea green.
Once you have changed your clothes, you should get your hair redone. You can do this at the hair salon near the general store in Falador. Here are the best hair styles:
Wind braids, curtains and long curtains are good for hair. As for beards: clean shave, handlebar, full mutton, full mustache, waxed and vizier looks the best. As for color, brown is the way to go!
If you want to do something else, then you can always buy black, adamant or rune (g) armour, it looks very fancy. But do not buy (t) armour because it isn't that noticeable.