No men's boards for you. They would all be too long. There are plenty of women's boards out there with decent graphics, you just have to look around. With your height, skill level, and budget, you may not have much of a choice. Troll ebay and check all the big online retailers, or buy from a cheaper brand.
A lot of salespeople will tell you the chin rule, but they are wrong. In general, a snowboard doesn't care how tall you are, it cares about how much pressure you are putting on it. There is no real way to "measure" your correct length. Get something in the high 130's if you want to try park or are particularly timid, and go longer if you want to ride all-mountain. As I said, I weigh just a little more than you and I ride a 141 and a 143. We could go shorter, but we'd start to lose stability.
Some suitable boards. I have starred some favorites:
Atomic Tika 139
Gnu B-street 141
Capita Space Metal Fantasy 143*
K2 Luna or Lunatique 138, 142*
Rome Vinyl 143*
Ride Compact 143
Never Summer Pandora 140, 143
Burton Troop 141
Burton Lux 139, 143
Atomic Fallen Angel 141
Boards from companies like 5151, Liquid, LTD, and Lamar are generally inferior in quality to the boards listed above. That being said, they may be more within your budget and will suit a beginner just fine. If you purchase a cheaper board, it's probably something you'll want to replace in a few years as you progress. A decent board would probably start at around $300. Consider buying used to get a better quality board on a budget. I bought my Capita Space Metal Fantasy used from a private seller for less than $150 and it's a great board in great condition.