If you don't know where to start, I'd suggest getting some mags and/or books about small space gardening, or container gardening, balcony or apartment gardening. I started with pics of plants that grabbed me and building a basic plan around those plants. The plan has changed quite a bit, but in the process I got to decide what I like the most. Another thing I did, which may be a tad too much for some, was get the Sunset Western Garden Book and read every.... single.... entry in the book, making notes, rejections as I went along. There is such a wealth of plant material available that I made rejection my first priority - my dog likes to bite into plants so toxic was rejected first. I live in a mobile home, so trees are automatically rejected. In my zone there is no frost, so anything that needs frost, like peonies, is a reject. This sorting narrowed the number of desireable/possible plants, and in the process led me to a lot of plants I would never have known about if I relied solely on the local big box stores for material.
I also went to every mail order site I could find to look over the plants available there, again using my rejection criteria - and have found some things I'm really enjoying now. I also have a number of plants that I've whipped out of their pots and tossed - either because I made a purchasing error, or because the blooms are not as advertised, or I just don't like them. Some have just gone gak on me for no discernible reason, but that happens to everybody and is just one of the fun parts of the game. I didn't mean to write a book. I just have such a great time with this container gardening thing that I want everybody else to do it too.