It absolutely depends on your wealth. The most straightforward thing to do if you're wealthy (for example, if you earn more than 2000 eur net a month and have no dependants), is to just use the public transportation when it is convenient and fast, but Uber and Taxify when it is longer distances or more complex routes. Taxify is cheaper when it is a very busy time, but otherwise Uber is much cheaper. Around central area you end up paying around 3 euros per trip, so if you use it twice daily for a month, it ends up being cheaper than owning a car, and more convenient. Uber drivers are nice.
If you live anywhere else from central area or even on the outskirts of the central area, or away from public transportation stops, it is wise to get a car, because the public transportation in Tallinn is truly horrible for anyone coming from another western European country. It is slow, unreliable time-wise, does not handle congestions well, smells frequently and is not very clean (most of the seats are dirty). Using public transportation for short routes or only within nicer areas is fine (e.g. the bus 1A is okay, the bus 23 not so much). Train is fine, but hardly usable because of the stops' location and lack of trains.
Oh, and parking is a pain, and expensive.