@EPawlick
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@EPawlick and Cole_Robbie
Cole_Robbie does have a point about juicy tomatoes. However, juicy tomatoes don't always spoil fast compared to non-juicy tomatoes—I haven't compared them to long-keeping tomatoes. If you give them more space, they should store longer than if they're packed touching other tomatoes (that could be particularly problematic for soft or juicy tomatoes). Large tomatoes are nice, because it's easier to want to display them (rather than just store them); so, it may be easier to be willing to allocate space for them as a result. Ventilation is good (even from below the tomato, if you can manage that). Plus, it's easy to tell when big tomatoes are ripening, because they're so big.
Whatever the case, most tomatoes, regardless of variety, should store without incident as long as they're green, for the most part. After ripening, regular tomatoes may keep anywhere from a day to a few weeks, or so, in my experience (while they may stay green for three or four months at the most, although many will likely ripen much sooner). However, some tomatoes can ferment if kept ripe in storage for a good while (without looking like they've gone bad).
Fruit flies do tend to lessen the storage life of tomatoes, and other fruits, if they're around in large numbers. They'll likely go for vulnerable ripe and overripe fruits first, but they're not overly picky with ripe fruits in my experience. Even unblemished tomatoes can go bad faster with them around. I definitely recommend keeping fruit flies at a minimum, if you can. Prevention is probably the best policy here, if possible.
Some tomato breeds will split or crack upon ripening. This is one of the main things to look out for when storing tomatoes, and in deciding which kinds you want for storage. However, some tomatoes will split or crack when vine-ripened, but if picked green they won't split or crack when ripened indoors as often. I think this is because the green fruit is firmer when picked (so picking it doesn't have as much potential to damage it). Some tomato breeds still reliably split on ripening even then, though.
Brandywine (if what I had was Brandywine) definitely isn't the worst tomato for storage, if picked green, and while it might not keep ages after ripening, I think it's a good choice out of the tomatoes offered by the vendor, particularly because of its size and delay in ripening (which I did notice at my friend's house). However, taste is also an important factor, and these taste pretty good, I think.
I went and read some reviews on it. It looks like it does split for some people. My friend who grew Brandywine didn't complain about splitting or cracking. I don't believe ones I grew that were probably Brandywine cracked or split. I'm guessing the growing conditions (soil, watering, and weather) are factors here.
Oh, another thing is if the stems are difficult to remove from the tomato, it's a good idea to use scissors to cut the stems (so you won't damage the fruit by pulling hard). Keeping the stems on can also help tomatoes to be tastier and in better condition after ripening, and if stems are difficult to remove, they might be easier to tie up and hang or something as can be seen in another thread that was recently active somewhere on the site. Keeping the stems on makes tomatoes less likely to dry up, too.
Your local climate, microbes, pests, and the place you store your tomatoes may have a lot of influence on how well which tomatoes store. The rules may be different in a humid area versus an arid area, also. I think soil plays a role, too (in the integrity of the tomato); how good a tomato is at using the specific soil and set of nutrients are also important factors, in my opinion.