I live in Dallas which has some pretty intense sunlight. I have an apartment with a west facing balcony. I'm sure I could grow some shade loving herbs here, but do you guys think I could grow some veggies here? I'm hoping with such intense sunlight, the afternoon sun might provide enough sun to do the trick. What do you guys think?
If you can get 6 or more hours of sunlight during the day, you should be able to grow vegetables. Keeping them watered might be your biggest challenge, if sunlight isn't a problem. In my climate, which is very rainy and sunlight is variable, I still had to water my vegetables in containers three times a day on sunny days--and once a day on cloudy/rainy days. After I set up a diy wicking system, I only had to refill the containers maybe every other day, which certainly saved me time; and also helped my plants grow better, as they weren't so stressed.
Ideally you can get very large containers. I used to use beverage tubs between 10 and 17 gallons each. The larger containers let me get away with watering once a day in the hot summer. I found several large plants in a larger tub did better than 1 plant in a 5 gallon bucket.
Ideally you can use something like a boot tray to keep water from going to the balcony below you. It will also let the plants suck up excess water during the day.
I have found that container gardens need extra feeding to keep the plant fruiting. I used worm compost tea, Neptune's Harvest and Espoma Plant Tone to feed my plants.
I made my own potting soil with good compost with peat moss or coconut coir. It is cheaper to buy components and mix your own potting mix.
I also would add a layer of mulch to the containers. The plants like it.