Having recently started studying a new opening, I think it's worth spending some time looking at what factors go into selecting and then learning openings. I discuss the evolution of an openings repertoire for experienced players in a companion post, which I think is a rather different animal than the process faced in choosing one's initial opening weapons, so it deserves its own discussion. Here I'd like to focus on the first steps faced by all of us as players, partly to provide a background on my own choices and also to help set the scene for how this affects opening system choices later on in our chess careers.
Although it's somewhat arbitrary, I'll define the initial process of openings selection as lasting until a player settles on the major system(s) as White for the first move, along with Black defenses to 1. e4 and 1. d4, that they will have in their permanent career repertoire. The above definition I think is generally a practical one, since it covers the essential decisions and challenges that every tournament-level player must face on a regular basis in the opening phase of the game. For me, this initial process lasted around a year.
When first learning chess in a systematic way, I tried out a number of different openings in informal games. In general, this is a great way to gain practical experience with the different systems' ideas and key positions, while also developing a gut feeling about which openings best suit you as a player. Now that good chess software is easily found, it is easy to test drive different openings with a willing silicon opponent, although I think the feedback you can get from a human opponent is very worthwhile, as long as you take their own biases into account. With the internet, it's also easy to find basic surveys of the various openings, to know what to try out. However, I think there's still something to be said for owning a comprehensive reference such as Modern Chess Openings (MCO) in order to be able to know what is out there and see the basic descriptions for all of the different openings, along with suggested variations.
As White, I initially opened with 1. e4 and after some experimentation chose suitable variations against the major Black defenses, playing the Exchange Ruy Lopez and Closed Sicilian in tournament play. Before that I had informally tried out the main Ruy Lopez lines and the Open Sicilian, but the complexity was at that point beyond my capabilities and inclinations. I recall being somewhat puzzled by the 1. d4 suite of openings and was never really attracted to them as White. The Reti (1. Nf3) was neat to try, but at the time I didn't really understand what White was supposed to do in it. (So that you have a frame of reference for my chess ability at the time, my first rating obtained in tournament play was in the low Class C range.)
As Black, I looked at a range of possibilities, especially for defenses to 1. e4. Informally, I played the Sicilian Najdorf, Alekhine, Closed Ruy Lopez, and French a great deal. After some time, however, I gravitated towards the Caro-Kann, after having a serious go at the French. It seemed to be similarly solid but without the drawbacks of the shut-in light-squared bishop and occasionally bare kingside. As far as defenses to 1. d4 went, although I dabbled some with the King's Indian, I settled on the Slav as another solid choice. Although the b7-c6-d5 pawn chain is a shared feature with the Caro-Kann, the positions arising from the two openings really aren't very similar, so the pairing doesn't save you much study time, unlike what you can achieve by playing the Modern (1..g6) or other very flexible openings that can be used against both 1. e4 and 1. d4. As a small bonus, however, the openings selection did mean that I never had to fear the Blackmar-Diemer Gambit (1. d4 d5 2. e4) since I could just transpose to a Caro-Kann with 2..c6.
While my openings selection as Black held up to the test of tournament play during my first year, I wasn't nearly as satisfied with my results with 1. e4. Essentially, I had discovered as Black that I played best and was most comfortable in semi-open positions. While the variations I had chosen as White also largely reflected this, I felt that I did not grasp their ideas at a fundamental level, plus my opponents were all obviously well-prepared (or at least better prepared) to meet 1. e4 as the most common opening choice. At this point I discovered IM Nigel Povah's How to Play the English Opening - a 119-page book published in 1983 - and decided to try it out. The opening concepts were explained in detail (or as much as a short book could contain), complete games were provided and the positions were new and interesting to me. I chose variations that I liked and after a few months of preparation permanently switched to 1. c4 as White.
There's a good deal of free advice out there on what openings are "best" to play, but I think it really boils down to whatever works for you as a player. (I have a similar view of approaches to chess training in general.) There is both a practical and an aesthetic dimension to this. The first one is easy to understand - if you regularly end up in losing or inferior positions out of the opening against players of comparable strength, then your openings are not doing the job of keeping you alive on the chessboard. Regarding aesthetics, if you don't have a genuine liking of the opening positions, or find your openings dull or incomprehensible, regardless of your results with them, they probably won't be a good permanent match for you.
Taking that a step further, I think it is ultimately preferable to buckle down and master an opening that you are genuinely attracted to, although you may be having sub-par results with it, rather than try to convince yourself that a boring opening with good practical results is in reality fun to play. (People's definitions of boring will vary widely; I think my opening repertoire is fascinating, I'm sure others would fall asleep looking at it.)
Finally, let's not forget that last part about fun, because unless you're a chess professional, fun has to be a component of the chess experience, otherwise it's just work. Chess improvement by definition requires work, but it should be the kind that leaves you with a smile at the end of it.