It's not that tricky to choose organic crops to grow on your small organic farm, but there are some important issues you should consider.
The first consideration for grower is to find crops that are well-suited to the local environment. For example, if you live in a short-season growing area, good luck getting watermelons to mature. It makes sense to grow crops that are already proven to grow well in your area.
Start with basic climate information. You can use the USDA Hardiness Zone Map to figure out general climate and growing conditions year-round in your area. Keep in mind that this popular map, while generally suited well to gardens and smaller farms, has some shortcomings too, especially for the eastern USA and areas west of the 100th meridian.
A zone map, while useful, doesn't tell the whole story of your specific environment. Your farm environment is affected by your actual geographical area, but also by your specific land issues. Is your site shaded, sunny, poorly drained, sloped, rocky, etc. What pests are lurking on your land? How will your soil quality affect crops? Do you have limited access to water?
Resources to help you choose the right crops for your location:
2. Space & Time
Obviously on a smaller organic farm space is limited. When space is limited, so is your time. For example, you could plant just fruit trees or grapes, but both of these crops take up a ton of space, are time intensive to care for and take a long time to grow. If you choose only slow-going, space intensive crops, that's probably all you'll be growing.
Equipment is another consideration. Some crops need more tools than you may have, or want to invest in. For example, if you decide to start a small row crop farm, such as field organic corn, wheat, rye or soybeans, you'll need more equipment than if you're growing basic veggie crops.
When choosing crops, consider if you'll need special, and/or expensive equipment to grow or harvest.
You may love organic bell peppers, but if you've got zero buyers in your area for this more expensive organic crop, you'll be sunk. Make sure you research organic buyers before choosing crops. Get a general idea about what folks in your area want to buy, what they're already buying and what they're willing to pay.
If every organic farm in your area grows a specific organic crop, you may want to go in a different direction to cut down on competition. For example, if farmer Bob and farmer Nancy, both down the road grow awesome organic asparagus, and have plenty of buyers, it doesn't make much sense for a new farmer in the area to choose peppers as a crop.
One time where it might make sense for you to grow the same crops as a nearby farm is if you're headed to the Farmers' Market, selling in another far off location or if you're opening a CSA, because in both cases customers will likely vary from other nearby farms. Another time it makes sense to double up on crops is if you have a specific request from a local buyer - say a restaurant or grocer.
6. Skill Level
If you're a new farmer you may not want to tackle organic cauliflower, celery or an entire field of heirloom tomatoes. Some crops simply take more skills than others to grow. Also, crop ease can vary greatly by the individual farmer. What you're good at and can handle, may be very different from what other farmers can manage. Research what it takes to grow various crops, including the sort of labor involved before you decide what to grow.
Obviously you don't have to adore every single crop you grow, but at least liking what you grow will help you out in the long run.
Crops you love are easier to educate others about (both buyers and employees), easier for you to talk up to buyers and if you really like a crop, you'll be more likely to see (and taste) when problems occur. Plus, from a pure happiness perspective, if you're going to make organic farming your life-long work, why not grow food you love?