If your climate is similar to Florida and you want to see some gardening success:
1. Use decent size containers min 14in - 16in up to 20in to give the roots room to spread and stay cool and moist.
2. It is all about the dirt - get moisture control soil to keep your plants happy.
Containers are important - the thick black ones from the nursery work well, so do quality pots - thin, cheap pots dry out too quickly and even if you water regularly it does stress the plant. You want happy plants:)
3. If you have at least five to six hrs min sunlight - you will be OK
4. The mint and strawberries like each other and they don't need full sun all day - you can put them in the shadier spot. To mix it up and make it more decorative, you can grow both mint and/or strawberries in a hanging planter and/or in a window box.
Nothing like having a couple of mints scent the air and eating strawberries from the window box.
5. Peppers love a lot of sun and they take a while to bear fruit, but if you like spicy I'd try a red chili pepper they do well and are super easy in a container. Buy the biggest containers at the dollar store - they have the cheapo, but nice looking plastic pots, just double them up to prevent the soil from drying out too quick.
I tried a new pepper variety this year called lunch box peppers, which did very well in a container, they are green at first then turn red. Lowes had them and they are not spicy - just really cute looking mini peppers. It isn't too particular as to sun and shade.
5. Tomatoes are prima donnas - they like to be fertilized and watered regularly, I recommend tomato tone, it is organic therefore does not burn the roots.
Look for "patio tomato" - at Lowes and Home Depot. Cherry tomatoes and Grape tomatoes are also good choices.
Pay attention to the label (before you buy:) - there are early varieties and varieties that take a long time to produce - it is nice to stagger short and long growing varieties if you have room for more than one.
Tomatoes and basil also like each other - basil is a good (easy) one to grow from seed, maybe try two different varieties. The sweet Italian basils struggle in the summer heat in Florida, but do fine in spring and fall.
If you have room for window boxes - seed a couple of different types of lettuces. Easy and pretty much guaranteed to succeed:) If it is too hot, give them shade or they'll shoot up.
If you can find a greek basil, tall and slim - it does OK in the sun, although the best of all is African Blue Basil which can get fat and happy and bushy and tolerates sun - it has a strong basil flavor with sort of a peppery slightly spicy flavor.
6. Having some shade may not be a bad thing at all depending on your climate. The first year I tried container gardening on a balcony everything got fried by the hot Florida summer sun. I didn't know then that veggies do better in the spring and fall in Florida. Nothing survives the brutal summers.
7. Rosemary is super easy to grow, loves the sun but will do OK in some shade - just give it a nice big pot and don't over water it:)
8. You didn't mention flowers - but I highly recommend bright orange cosmos and zinnias for some color. Grow them from seed - very easy.
9. Last suggestion - if you like herbs - get some lemon verbena, it has a lovely sweet lemon scent (when you crush the leaves), you can make a cup of tea from the leaves or add it to fish, chicken and pork for seasoning. Also a great drink garnish and nice addition to ide tea.
Lowes will not have it - but a good garden center-nursery will. You can always look up a couple of garden centers and call them before you make that trip or you'll come home with a bunch of plants and none of them what you came for:).
It doesn't like the cold or windy conditions so put it in a sunny and protected spot and give it plenty of water:).
The second-year I had a balcony garden I bought a red passion flower and grew it around a cheap $25 metal garden arch, the kind they use as wedding arbors. You can get them in white or in green (at Michaels and some garden centers) or spray paint it turquoise like I did:) - I used some X-mas lights and set up a mini table and chairs - nice spot to have a glass of wine or your morning cup of coffee.
Go vertical for privacy if you can or just use a trellis on the wall for peas or beans (probably too late for that now), but you might try sweet potatoes they like to climb, both the real sweet potatoes and the ornamental ones.
I found a rectangular outdoor table at a thrift store - it was long enough to take up the entire breadth of the balcony on one side. Then I arranged my plants, flowers and some doodads in an eye-pleasing fashion at different heights - voila - a pretty container garden.
A table has the advantage that you can store all your garden gear underneath - out of sight. Or make it the outdoor kitty condo or outfit it as a fun play space for a toddler with a carpet and pillows ...
If I were you I would locate a nursery that specializes in local plants and herbs and talk with them about what works well in your area.
Think evergreen - use evergreen plants to give your mini garden structure and good looks year around. Palms and hanging spider plants are super hardy, always look good and don't break the bank.
You can join local FB garden groups - you can trade, get plants for free or exchange information.
For the pots I'd definitely try one of those free cycle groups.
Sometimes you can find a gift basket of mixed evergreen plants on sale at the grocery store - a good way to get six nice plants or chat up a neighbor who has nice plants and before you know it you are leaving with an armful of baby plants:).
When you know someone is moving out you can often score as well and our local flea market has an awesome plant selection - from fruit trees to onions they have it all.
Good Luck!