As a bunch of people have already said, first pick a miniature you like and are interested in painting. If you don't do that, then you're not going to be inspired and won't put in the time and attention needed for a good competition piece.
That being said, if you're anything like the rest of us, I'm guessing there are a lot of minis that into that category. So, look a piece that also...
a) shows off your abilities. Ask yourself what are you good at? Freehand, faces, metals, weathering, etc? Pick something that plays to your strengths.
b) is a preferably dynamic and interesting sculpt. Champions, generals, standard bearers, etc then to do better than random grunts. There's usually more detail and they're most interesting figures.
c) is a high quality figure. While top artists can find a way to make almost any figure look good, why not cut yourself a break and just pick a nice figure to start. If you like warhammer, maybe look at grabbing a forgeworld figure. Or, better yet, find a company that just makes display figures. Scale75, Nutsplanet, Studio McVey, Nocturna, Ares Mythologic, Andrea (Warlord Sage and Dark Nova lines), and many many more. Check the CMON store, they have some of these brands and many others too.
d) tells a story. This can combine the figure, the painting/weathering, and the base. Think about what the figure is doing. Are they in the middle of a battle? Are they exploring a dungeon? Are they fleeing from a monster? The possibilities are endless. Come up with an idea and then think of little clues you can add to the paint job, the base, etc that help tell that story.
Now, you don't need to check off all of those. But they're good things to keep in mind when you go about finding a piece to work on. It can also be useful to look at what sort of figures have won at past competitions. Check out Crystal Brush winners. The Draconic Awards also posts past winners on their site. Don't copy from past winners, but use them to help inspire you.
