Common tmato: Lycopersicon esculentum
The origin of the word tomato is Latin for 'juicy wolf peach' because they were believed to evoke warewolves, and were initially believed to be poisonous (and despite being proven otherwise, some people like to hold onto the belief that they are still poisonous to avoid eating them... unless they're made into a sauce). They only became popular in the early 1820s after it was discovered they weren't poisonous, and became exceptionally popular in the 1920s when they became widely cultivated.
Its is a common SCA myth that tomatoes were not available in Europe in the SCA period (pre-seventeenth century).
In fact, as with many New World (read North and South Americas) foods (like chocolate), it was in fact known, and utilised, if in different ways to the modern palate. If anything, its rarity value made it more of an expensive novelty to start with.
They were known as "Golden Apples", and were for example eaten as follows:
"The golden apple one eats in the same way as the eggplant with pepper, salt and oil, but it gives little and evil nutrition." (Source: "Herbario nuovo", Roma, 1585, dall'introduzione di Piero Camporesi a "La scienza in cucina e l'arte del mangiare bene" di Pellegrino Artusi)
For an excellent discussion on tomatoes and their use in the SCA period, read this excellent article available at Stefan's Florilegium: http://www.florilegium.org/files/FOOD-VEGETABLES/16C-Tomato-art.html
If, for some bizarre reason, you want to grow tomatoes, they're apparently fairly easy to cultivate. You can readily buy seeds and seedlings from the supermaket or Bunnings, and you should plant them in full sun so they get plenty of water. You may have to fight a number of tomato problems such as anthracnose, bacterial canker, black mould, curly top, early blight, root rot, powdery mildew, southern blight, infectious chlorosis virus, tomato pith necrosis, water mould, white mould.
There are also lots of insects which like to munch on your tomato plant, such as: lygus bugs, potato tuberworm (they've clearly become confused), stink bugs, fruit worms, pin worms, leafhopers, aphids, leaf miners, mites, cutworms and symphlyans. Nematodes will also have a fun time with your tomato.
There are many tomato varieties (non-hybrid) such as: