Larger magazines will consider novellas; the problem is, since a novella is going to take the same space as two or three shorter stories, it has to be as good as two or three other stories for them to want to include it. Smaller magazines generally won't consider them at all: even the ones that have generous length limits usually cut off around 10k words, and there aren't too many that'll go that high.
Anthologies are generally by invitation, so you pretty much need to be known–at least by whoever is putting the anthology together: another good reason to be active in convention circles–in order to find out about these at all. (That is, unless you're entering one of those "contests" where everyone foolish enough to pay the reading fee gets included in the final product… and then you're obliged to buy an exorbitantly-priced copy in order to ever see your own story in (eight-point) print, more copies if you want your family and friends to. In other words, they're vanity presses for shorter works.) There are exceptions to this, but you usually need to regularly read writing magazines to catch the announcements. (And then check them out carefully to make sure they aren't scam artists like the above.)
On the other hand, you're never "necessarily limited to self-publishing." Quality will always get you considered–sometimes even in violation of length limits; assuming the quality is there, persistence will eventually get you placed.
There are also professional publishers who will consider novellas for ebook publication, so even if ebooks are your prime option, you can still work with a publisher and get it done the traditional way. Novellas are definitely harder to market than novels, because they are generally juicy enough to all-but-warrant an individual book, but few would buy one individually. Online magazines aren't a bad bet, since they don't really have page count limits.
In all seriousness, your best bet might be some form of digital publishing. The numbers of print novellas bought each year are very slim; it's a lot easier to sell a novel than a novella, in print.
In digital, novellas (that 20-40k word range) and short novels (say, 40-60k give or take a bit) both do pretty well. Whether you self publish (more work, keep all the profit) or go to a small press focused on ebooks (there's a lot of them, and a bunch who accept shorter works, but check reputations first), it's a viable way to go with this length.