As others have said, it depends on many factors, including the type of relationship, your level of maturity, and so on. However, at 15 your primary job is still to finish up things such as school, and maturing physically, emotionally and intellectually, as well as to start thinking about what you want to do with your life.
Right now, one of the most important things you need to do is work on creating a feeling of stability in your life. Your parents’ divorce will affect your day-to-day life, but it will also bring out all sorts of emotions, too. Some will be related to valid feelings of betrayal and fear of change, while others may derive from a mistaken feeling of guilt for possibly contributing to the break up (you are not at fault).
Thus, good friends will be an important source of support right now, but undertaking a relationship during a time the rest of your life has been turned topsy-turvey is not wise. As Shakespeare said, “The course of true love never did run smooth,” and that is the truth. Emotional upsets are part and parcel of relationships, especially when you are in your teens, and that may simply be too much stress right now.
In any case, I discussed this with my daughter when she started high school. She concurred that hanging out in a group was the simplest and least disruptive thing to do when she was 14 and 15. She began very carefully to date at age 16 but didn’t settle down with “the one,” and she still hasn’t at 17. She does have many good and close friends, both male and female, but she intends to go to college and then medical school, and she wants to be able to focus on those goals right now.
Lysander:
Ay me! for aught that I could ever read,
Could ever hear by tale or history,
The course of true love never did run smooth;
But either it was different in blood—
Hermia:
O cross! too high to be enthrall’d to low.
Lysander:
Or else misgraffèd in respect of years—
Hermia:
O spite! too old to be engag’d to young.
Lysander:
Or else it stood upon the choice of friends—
Hermia:
O hell! to choose love by another’s eyes.
A Midsummer Night’s Dream Act 1, scene 1, 132–140