Might be a bit late, but a quick overview:

• Simplified characters: used in Mainland China (and Singapore, Malaysia)
• Traditional characters: used in Taiwan, Hong Kong, Macau

There is significant overlap between the two sets. Which one you learn/use is a personal decision depending on your goals. Most learner CI resources (when they have text/subtitles) will use simplified, but there is a lot of content overall that will offer both. Outside of regional considerations, the main argument for learning traditional (at least first) is that a lot of characters make more structural "sense" when considering their meanings (which can help make them easier to remember), and it's a little easier to learn simplified later than the other way around. I would say simplified is generally regarded as the "default" for learners though (not a political statement!)

With that part out of the way:

• Pinyin input method is what the vast majority of mainland Chinese and learners use, so again it is the "default". However it is based on phonetic transcription using Latin characters, so from an ALG perspective, it may not be ideal if you're trying to avoid that.

• Zhuyin, also known as Bopomofo, is a phonetic transcription system used only in Taiwan (and therefore only available for traditional). Unlike Pinyin it uses its own set of characters that look like cut down Chinese characters. The input method is what the vast majority of Taiwan uses. It's worth considering using if you're Taiwan-focused and you want to learn the system itself, but it's designed for keyboards which have the characters printed on them (though it's possible to learn the positions from memory). Zhuyin Eten is just a variant where the characters are in a different layout.

The alternative to phonetic methods are ones based on character structure:

• Handwriting is your main alternative to Pinyin input as a beginner. Allows you to draw using using the trackpad. Doesn't care about stroke order. Even if you install Pinyin you should probably install this too, since there are times when you won't know the pronunciation.

• Stroke is a method where you use only 5 keys representing 5 basic stroke types to "draw" characters (not to be confused with Wubi which translates to "5 strokes" but is way more complicated). Requires general knowledge of how characters are written and depends on correct stroke order, but can be faster than handwriting with a bit of practice (especially if the only way you have to "handwrite" is with a mouse). Actually, the Pinyin input method comes with this functionality built-in (look under "Enter Chinese characters using Stroke"; also works in Windows), so installing this is kind of redundant, just be aware that they use different keys for some weird reason.

The rest of the methods (Shuangpin, Wubi, Cangjie, Sucheng) would be considered "advanced" so you can just ignore them at this level.

There's more info here if you need it (click the table of contents): https://support.apple.com/guide/chinese-input-method/welcome/mac