Most berries will need large pots, both to accommodate the roots and to balance the mature-size top of the plants. Large pots with large plants can get very heavy. If you think you will be moving the containers, either indoors for the winter or around the patio, place them on a sturdy plant dolly. Of course they will also need plenty of drainage holes.
If you plan on leaving your plant outdoors for the winter, choose a material that can handle your weather. For cold, frosty zones, wood, heavy duty plastic or the newer resin and fiberglass materials are good choices. Most will be labeled as frost tolerant, if they are.
Birds and other creatures love berries, too. Most gardeners will need to provide some type of protection over the fruit, as it starts to ripen. Bird netting or cages built with chicken wire are popular choices. Make sure the netting is held up off the fruit, or the birds will reach right through. And don't wait until you see the fruits ripening to cover them. Birds have different tastes than we do.
Growing blueberries in containers makes it easy to keep the soil at the low pH blueberries need to grow well. There are special potting mixes for acid loving plants or you can make your own blend of half regular potting soil and half peat.
Blueberries can live a long time, so give them a big container at the start. Something at least 2 feet wide and deep, with excellent drainage. Plant them so their roots are just below soil level and then add a 1 - 2 inch layer of bark mulch.
A sunny spot is ideal for most potted blueberries, although where summers are unrelentingly hot, afternoon shade is welcome. All blueberries like regular water. They do no fruit well if they bounce from drought to flood. They also do not like to sit in wet soil for prolonged periods.
You will want to have at least 2 bushes that bloom around the same time, for good pollination and fruit set. To extend the harvest season, You could plant additional containers and choose early, mid- or late season varieties. Blueberries may start fruiting in their first year and each additional year they should become more abundant.
Both currants and gooseberries fruit on branches that are 2 and 3 years old. That means you will need to prune out the oldest branches each winter or early spring. You wan to aim to have a mix of 2 and 3 year old branches along with the new seasons growth, which will fruit the following year.
They'll need plenty of sunshine, to ripen. You'll know they are ripe when they change from green to whatever color they are supposed to be (red, black, pink or white). Green gooseberries will turn more yellow with stripes and become a bit softer.
Regular water will help the berries plump up. Feed with a water soluble organic fertilizer every 2 - 4 weeks
Traditional blackberries are a tangled mess of thorny branches and don't adapt well to containers. If you want to try blackberries, choose a thornless variety. They'll be easier on your skin and can grow without trellising.