According to research it's approximately a 2% chance of getting side effects from Finasteride. However, there are many claims and anecdotal evidence that it may be higher, possibly up to a 5% chance. It's near impossible to say what the exact chance of suffering side effects from Finasteride are, but there is no doubt something negative happening is very low.
The important thing is, it won't hurt to try Finasteride. If you do experience side effects, you can always quit the treatment and they'll subside. There are people who may attempt to scare you away but I highly suggest to not listen to these individuals, who say side effects won't subside even when Finasteride is stopped. No real evidence has been shown about side effects continuing to persist when Finasteride is discontinued.
Take me for example, I take Dutasteride, which is basically a stronger version of Finasteride. I've been on this treatment for a little over two years now and have greatly benefited from it. No problems have ever occurred and I just haven't experienced any of the horror stories. Dutasteride has given me good results for someone who suffers from severely harsh Male Pattern Baldness, and my confidence improved from that alone. At the end, in the times we live in, it's up to you on what can be done for your case with the available options we currently have.