Hi & welcome to Gardenweb!

You can find your gardening zone here by typing your ZIP code in the box, hit enter. If you add that to your profile, it should show up next to your name when you post, so people will be able to give you more specific advice that works in your climate.

Are you looking for a summer display, or do you want to have stuff that grows all year? What do you like? Flowers? Veggies? Cactus? Beautiful leaves? Full sun plants can need water about every day during the summer, so knowing generally if you're usually around, don't often take business trips, would be helpful too.

Hi, Kat! Yes, figuring out your zone is a good idea. You may also look into the Sunset gardening book and figure out your Sunset zone-- those are really more detailed and sort of a standard for CA gardeners.

That said, before you buy containers, you need to consider what you want to grow and weight. Find out if your condo place knows the weight limit of your balcony. Also, if you decide to grow certain veggies like curcurbits, you'll want more root space than, say, a miniature pepper.

And if you want to grow perennials, make sure to choose varieties that are one or two zones lower than yours (USDA zones), as they can take less cold (or actually freeze/thaw cycles) in pots than in ground.

Strike what I said before... I just realized you are from the SF bay area, so I guess not much frost there, right? San Francisco would make you a zone 10, I think. -Lucky you, you have a HUGE choice of things you can grow. The question is probably more, what kind of exposure do you have? You say full sun... does that mean your balcony is facing straight south? Where in the bay area you are, might also have something to say. From what I have heard, SF is a bit weird, when it comes to micro-climates. Some areas are very dry, while others are a bit more humid, with fogs and showers (that·s what a guy from SF told me 18 years ago, anyway). I·m going to imagine that you live in the dryer part in the following, as it would be easier to adapt to the more humid part, than the other way around (things in pots dries more easily than stuff in ground).
Afternoon sun can be harder on the plants, than morning sun is, so if your balcony is facing south, I would provide some shade at least on the east end.
First of, you might want to buy (or make some) self-watering planters, as you might otherwise have to water both morning and evening during the summer months and still struggle a bit to keep healthy plants, unless you plan on only growing cacti and succulents. -I think self/watering pots would be particularly good for most herbs and veggies. And the bigger your pots are, the better. Earth-boxes would be great too (can also be home-made). That said, succulents are not a bad choice on a full sun balcony in zone 10. I would get some that where fairly dense and fast-growing to provide some shade for the less heat tolerant plants, if I where you.
What kind of railing do you have? Concrete? Metal bars? -If you have metal bars, I would put window boxes with something that trails down, and can withstand the hot temperatures and drying out now and then. Ice plants (Carpobrotus edulis) might be a good choice. They grow quite fast (for a succulent), have fleshy leafs and stems, and loads of flowers, that are open during the day, while the sun hits them. Long blooming period as well. And apparently you can also eat them, but I·ve never tried that, so I can·t say what they taste like, if they are good, or how to prepare them. Then in between them, or in a separate box on the inside of the railing, I would probably grow something that has a more erect growth habit. ALSO something that can withstand some heat and a bit of drying out... window boxes dries out easily, unless they are VERY deep, and I would think that even self-watering ones might do so too, on a southern balcony railing without shadow where you live. Do you have an overhang/ roof on your balcony? Then I would hang some planters, with even more stuff that could provide shade. An aloe vera that was often left to dry out completely, would trail a bit instead of being totally upright, I think. That·s my theory anyway. You don·t have to make shade on all the balcony, but a shaded area would not be a bad thing. Not only for plants that dislike the heat, but it might also be a good place for a sitting arrangement.
Other ways to provide shade would be some heat/tolerant bushes in big planters on the ground. Eucalypstus perhaps, or a Bougainvillea? An Orleander is also very pretty (though, you should be aware, that they are very poisonous if ingested, so not an option if you have small children or pets around). If you have a palm or a pony tail inside, you could move that outside as well.
A solution that could save some space, would be a vine on a trellis, perhaps a passion-fruit (passiflora). You could plant some runner beans like hyacinth bean vines or borlotti beans with it the first year, until it gets more full. The beans also adds some nitrogen to the soil, which might help the passion-fruit grow faster (not that it·s a slow grower, though). And then you can also eat both the beans and passion-fruits. The passion-fruit is a perennial, and would give you both flower and fruit most of the year... There are many varieties, with colours in red, pink, violet and blue. and fruit in different shapes, sizes and tastes.
Now that you have some shade, I would say that you can grow almost any vegetable or herb that you like. Some might not grow well in the summer (e.g. radishes or lettuce, that you can grow earlier or later in the season), others will grow very happily in the dappled shade, like most basil or some cales. you could probably grow two crops of basil... just sow some new ones, when the old ones are beginning to flower (the flowers can also be eaten, they are a bit sweeter than the leaves, but it is a sign, that the basil will be gone soon). Tomatos actually love sun, but they HATE drying out, and are very thirsty, so some light shade wouldn·t be a bad thing, especially in the afternoon. Chillies can go to the front of the balcony, and provide a bid of shade to other things as well. Make sure they are well watered, even if they can withstand drying out slightly now and then. Oregano could also go in the sun, and possibly lavender or hyssop. Just make sure the pots are big enough. Artichokes would love it on your balcony, I·m sure. In fact, I would say that you could grow any kind of vegetable, that you might find in the Mediterranean kitchen, or Thai kitchen or Indian... With your zone, I would think you could get several harvests in a season, if planned right.
Some Kiwi vines, a peach, a lemon or even an orange tree would probably do very well. and they would provide even more shade, hehe...
If you have a balcony with concrete around it, I would say that you are better of to begin with... It would make it much easier to provide shade.
Always remember, that your plants are in pots... If they don·t thrive in one place, you can simply move them around. Perhaps someone from a warmer zone than me, has better plant suggestions that I do.... I basically just tried to remember what I·ve seen in Greece and Italy.
Oh.... LEMON VERBENA!!! I would definitely grow a lemon verbena (Aloysia citrodora) So very good in poultry and fish dishes, in desserts, in teas (e.g. with mint and lemon), in cold drinks and coctails (lemonade, mohitos etc.), and very pretty too... Whether it would prefer a bit of shade or full sun, I don·t know... But I would get it, and try to find the right spot for it.... If it gets too big, simply eat it, or rub it all over you!!! SO delicious and fragrant!
Good luck with it, and let us know how it turned out! And also let us know if there is anything you need help with.

Jesus, I dunno what to add to what VG already listed out in such detail, haha, but since she requested I take a look at this thread.... South Bay is really quite hot in summers. But like all others said, knowing which direction you're facing would help folks make suggestions--and also knowing if you have an overhang/cover would be useful.

Assuming you live in the SJ vicinity, tomatoes would work wonders there. I used to plant them in Pleasanton each year and spent more money on gas delivering buckets of tomatoes everywhere because there comes a point at which one can eat no more tomatoes, no matter how organic or how healthy and delicious. Roses, with modified soil to make more acidic, also grow nicely in that sun; a larger container with spacing for spillers would be nice (petunia?). Unless you can find some filtered sun or shade for it, I would avoid the lettuce or really leafy things unless you do it now....as in like today, haha. All peppers and most herbs will work.

As you place plants out with different layouts on your balcony, you will figure out where you do or don't have shade. Like me on my southern balconies with overhang -- I have plenty of full sun spots but a surprising amount of bright, bright shade. And...over the course of summer, through scorch, die and revive tactics, I will figure out that these full sun plants actually can't handle it, or the shade plants plop over and die despite having been put in shade. I have a couple of racks and a bookcase placed sideways right now so planning out the space changes near daily haha.

As VG suggested -- if you want flowers, definitely consider bougainvillea. I'm currently contemplating if I want to give up part of my railing to this full sun beauty....but this one definitely thrives in full, full sun.

Hope that helps!