You can order seed potato pieces from an online catalog, but i use store bought organic potatoes and they do just fine.
This is what I do. If I can find some potatoes that are already growing sprouts I will buy those. But if not I buy whatever kind of potatoes i want to grow, white, russet, fingerlings, red, etc.
I cut them into about egg size pieces or leave whole if small, be sure each piece has one or two eyes. Let them heal on counter for about one week. In the meantime I prepare my raised bed, that is how I like to grow them. I fill it with good soil and compost or amend with new compost if I am just replanting. I dig trenches about 12″ deep and plant the pieces cut side down, eyes up about 10″apart, covering them with 4″ of soil. As the greens grow I continue to bury them until I reach the top of the 12″ . Do not let the potatoes grow above soil, keep them buried to prevent greening, green potatoes contain a poison called solanine and are not healthy to eat. I water them just like the rest of my garden.
Depending on size and type of potato they usually take 80-115 days. You can dig around to see if they are the size you want. They can be harvested small or large. A good way of telling is when the vines die, stop watering and leave in for 2-3 weeks to toughen the skin for storage or eat fresh.
Once you grow some you will say , like I did… That was so easy!
Note; I do not recommend growing them in barrels, everyone I know that has they have rotted. Florida is to humid I believe.