You can place your garden wherever it works for you, just be sure you have enough light. If you do not have a space with ample light for your plants, you can use HID, high intensity discharge, lights to grow your potted friends. The best locations for your shelf or table of plants is one that has durable floors such as tile. If you much place your garden on carpet or wood, put down plastic or a tarp to protect your floors from water damage. Whatever you decide to grow, plant it in potting soil specifically designed for indoor plants.
Herbs are great for growing indoors. Just fill a pot with the right type of soil, plant your chosen herb seeds, and place in an area that sees approximately six hours of sun daily. Tomatoes are also wonderful to grow indoors. Cherry and grape tomatoes are the best for this and you can even grow tomatoes upside down from the ceiling if you don't have a lot of extra space.
Salad greens are another tasty option for your apartment garden. They're easy to grow and are short-season crops, meaning you can continually harvest them by just planting a little more every couple of weeks. Lettuce does need to be in soil that is moist throughout without being soggy. Watering from the bottom using a watering tray every other day will work in most environments.
Radishes are simple to grow, so they make a great choice for beginner gardeners. You can grow them in almost any pot that's at least a foot in diameter. You'll have radishes ready to enjoy in 3 weeks and can continue enjoying them by just planting more every week or two.
Finally, green beans can be grown indoors, but they do need at least six hours of sun a day. If you don't have that level of sun, grow lights can do the trick and you'll have tasty green beans to eat in a couple of months! Happy gardening!