It's hard to say I've seen people do their own hair/get a friend to do it and sometimes it turns out great and sometimes.. well, it doesn't look the best. Personally I would go to a salon myself, It's up to you though just make sure she knows what she's doing and has done a good job in the past.
You asked a question about a month? or two ago about your looks. We all love your eyes and think you have a great face. Go to a salon and find the best stylist there and tell her to do what she would do if it was her hair-color-style
I'd say it depends on what color you're going. If I'm doing my hair just simple brown or roots cover up, I do it at home, but I get the proper sh*t and invest in some brushes 'cause they make ALL the difference.
But if you're going for a pretty serious change in color, go to the salon, they know what they're doing.