I am not an expert, but I am going to write up what I think. Note that there is a Coffee Stack Exchange if you later have non-health related questions about coffee.
Caffeine has some positive effects, but also some negative effects.
The positive effects seem to be linked to better mood and concentration, and preventing a number of cancers and Type II diabetes. It also improves athletic performance a tiny bit, especially when working out in the morning.
Ironically, the same article mentions that caffeine may decrease people's mood by making them anxious and disrupting sleep patterns if you take it too late in the day. It raises blood pressure levels make it harder for people with Type II diabetes to manage their insulin levels. Coffee is also a mutagenic.
So whatever health positives there are, there seems to be a risk for the opposite to occur, which is a bit paradoxical. Coffee contains antioxidants, but it's also a laxative which may inhibit uptake of nutrients. It may upset your stomach. It may stain your teeth over time. There are also some other effects (good and bad) you can read about.
There is also the finding in rat subjects that coffee only makes the "lazy" motivated, but already motivated subjects are actually hampered by the stimulant.
The health benefits your friends are referring to, I think are dubious. If you don't even enjoy coffee, I think the net effect may even be negative for you. There is usually a peer pressure around drinking coffee (because it is a stimulant drug), and maybe they just want you to join in.
I am a coffee drinker, and the main reason I drink it is because it gets me alert in the morning (and I have learned to enjoy the taste, which is a positive). I also use it as a short-term mood booster to get back to work, if my morale starts to wind down. But on the negative side is that it can make you jittery and anxious, and the motivation gained is followed by a "crash" where your concentration and mood will slip.
Coffee does not provide concentration over an extended time, so any cognitive performance increase will be short-lived. Basically, caffeine will only help you work longer if you are already tired, but it will not improve cognitive performance if you are already energized. Think of it as a 2 am quick fix, not an 11 am booster. It will however probably improve physical performance a bit whenever.
From your description of yourself, I would not start. You do not seem to need it, in any practical way.
Regarding tea, it usually contains some caffeine (there are caffeine-free teas), but it may also provide more antioxidants. It may be a better health choice than coffee.