I learned and used zhuyin as a child and one day in my late teens I decided to learn pinyin to see if I could type faster with it. I learned the rules of pinyin in 10 minutes and could accurately and comfortably type with it by the next day. The point is that pinyin is easily picked up once you have learned zhuyin. So I think if you want to kill two birds with one stone then you could try learning zhuyin and then pinyin.

You said that in pinyin, the "an" in "tian" does not sound like "an" by itself. Well, in zhuyin, "an" and "tian" would be "ㄢ" and "ㄊㄧㄢ", respectively (notice the "ㄢ" in "ㄊㄧㄢ"). So this idiosyncrasy was already present in zhuyin. I say already present because pinyin is derived from zhuyin. The Scheme of the Chinese Phonetic Alphabet (partial text), passed by the National People's Congress in 1958, introduces and specifies pinyin in terms of zhuyin. As you can see, before the simplification and prefix rules, with the exception of -in, -ün, ing, -ong, and -iong, there is a one-to-one mapping between the symbols of the two phonetic notations, The point is that zhuyin does not offer that much different of a conceptual model than pinyin does. If your source, however credible it may be, claims that you could learn zhuyin in one hour, then you could probably learn pinyin in one hour. So, now, do you want to learn the one that uses a completely alien set of symbols, or the one that uses symbols that are already familiar to you but that you have to learn different phonetic values for? Remember that English and French use Roman letters in different manners as well.

Really, however you decide, your choice for the notation for how Chinese characters are pronounced is one of the lesser concerns in your journey to learn Chinese.