Head into the town area, and hold down F12+N+R+Q. Release them and cancel out of that screen. When you go back, you'll be able to access Mad Eddy's and the Beta Shop, which will give you free money, allow you to purchase rare/event items, and allow you to skip months or years.
The easiest contest to win in your first year is the art contest.
Every so often, after an art lesson, you will be offered the chance to paint a picture for 100g. Only do so if your daughter's art skill is above 90 points, as the picture will be the same as her stat. That one painting will allow you to win every art contest with no more work whatsover.