There is nothing surprising to be expected here. The most popular brands of soft drinks and natural juices can be found in every store.
We have many local brands of soft drinks too. In most cases you won't find them in bars and restaurants but only at grocery stores. Those can be very cheap, something like ?0.3 for 2 liters bottle.
Tea and coffee are available everywhere for prices starting at just ?0.15 and going up to ?2.50. In most places people don't have much idea what a good coffee or tea is, so don't expect wonders.
Don't be surprised if you ask for green tea but receive black for example. Note also that most Bulgarians make no difference between tea and herbal tea.
Coffee is usually machine-prepared and it's unlikely to find Turkish coffee in casual places. Of course there are few good and more expensive cafes which can make good coffee and offer big variety of tea.
Many fast food shops and kiosks offer ayran (kefir). It's almost always available in donner kebab shops for example. It's supposed to be made with the (famous?) Bulgarian yoghurt but don't rely on this too much.
Many tourist guides will tell you to try the (I'll use this word "famous" once again) boza. In reality it isn't as popular as it used to be, and isn't as good either.
It's worth trying mostly if you find a place where boza served with pastry and prepared locally, not bottled. Note that the boza has minor alcohol content (around 1%).
During the cold season you can find sauerkraut juice mostly at the outdoor marketplaces. It's an interesting and healthy drink but don't drink too much of it to avoid stomach problems.