僕 is not childish at all as far as you are a male person and referring to yourself. If you are a female person and use 僕 to refer to yourself, it sounds like you came out of an anime program. But the thing is that if you are with your peers and then use 僕, (depending on your age and who your peers are,) you might sound a little too childish or naive; you might want to use 俺 instead. When I'm talking with my friends from high school, I always use 俺, but when I am talking with my c-workers, I usually use 僕. 私(わたし) is always acceptable almost in any situations, but if you pronounce 私 as わたくし, it sounds professional and formal. The use of 自分 as to refer to yourself (or your interlocutor) varies from region to region and age to age; in some regions in Japan, 自分 is used to refer to your interlocutor rather than yourself. And if you are talking to older people and if you use 自分 to refer to yourself, to me, that sounds a little obsolete; to me, it sounds a little like "WWII era" thing. But in Japanese, personal pronouns are not used very often. So it is very possible that when 自分 is used to mean "self", it may look like the personal pronoun "I". e.g. (私は)自分でお皿を毎日洗います。-- (I) wash the dishes by myself everyday.

Using 僕 isn't childish at all, there are old men who use it. However, in the formal situation, using 私 is appropriate. Yes, you can use 自分 as "I" in the informal situation, but I would never like recommend you personally. Please wait for ther opinions. Anyway, I hope this helps you.