I'm 25 years old...
Some people around me talk that it's too late for me to start learning martial art now, but I want to give it a try.
I personally started Taekwondo when I was 27; 15 years later, I'm a second degree black belt and still training. In the school I train at, we have a gentleman who started after he retired (mid-late 60s). He is now a 1st kup (one away from black belt) and in his mid-70s!
25 is not too late (nor too early) to start a martial art! Within the wider organisation, there are many examples of students who started rather later in life than 25 and all are very capable martial artists.
stretching my body is really, really killing me, I cannot touch my toes while sitting straight
I couldn't touch my toes (either sitting or standing) when I started. Although I'm significantly more flexible now (after 15 years of training), I still struggle to bend that much! However, I don't need to be that flexible; I can produce powerful techniques without being able to tie myself in knots.
I won't offer advice on which art to train in because I'm biased and have no experience of Hapkido or Wing Chun. As other answers have pointed out, it is important that you focus more on finding the right instructor and school, rather than an art.
So, don't worry about your age or flexibility, but do concentrate on finding the right instructor and school.