When talking about Japanese formal language, it gets tricky because there’s essentially 3 kinds.
Teineigo 丁寧語 polite form
Sonkeigo 尊敬語 honorific form
Kenjougo 謙譲語 respectful form
Keigo explanation here
This article explains the differences very well, but essentially teineigo is what we all learn when initially studying Japanese - using -ます form and -です. I think this would be the appropriate default form to use as it’s just general politeness to everyone.
Sonkeigo is a step above and uses different verb conjugations entirely to treat the other person with respect. Student/teacher, worker/boss, waiter/customer - in all these relationships the former will adjust their speech to treat the latter more respectfully.
Considering we’re all equal here, it would be weird to use though it wouldn’t be absolutely inappropriate for the moderator of a thread to use if they want to be extra respectful. The downside is it also creates distance in relationships.
Kenjougo is similar to sonkeigo in that verb conjugations are completely different, but focuses on adjusting the language to make yourself sound more humble. It tends to be used in conjunction with sonkeigo, but I feel it would be entirely inappropriate here. Not to mention (according to the polls) very few of us can use it or understand it.
It tends to be used to create good first impressions when introducing yourself at work, or if you’re a customer, a service provider will use it on themselves to make you feel "special. "
Long story short, if you want to go the formal route, polite form makes sense. And if we go by the assumption that most of us learned Japanese from a textbook and not through casual conversations with friends, it should be easier for most of us to understand.
If your personal goal is to practice using an aspect of Japanese you don’t get to practice anywhere else (ie casual, short form), then I still think book discussion posts can be whatever makes you happy.
The thing with casual language is, there’s also a wide net in terms with how casual you want to be. My first post for example was written with the intention of making it more “textbook learned” appropriate vs more chat speak (for example, 思っている being shortened to 思ってる) . If you choose to go more chat speak, it might be hard for others to understand such as cutting out particles and subject, etc.
Again, whatever helps you with your study can be your go to, but if you’re participating with the intention that you hope someone will read your ideas and respond to them, then maybe you should adjust your language to make it easier for others. Just something to keep in mind.
I also meant to add an end note to my last post, but one of the words I struggled to find a word for is “forum post” since it can be used interchangeably with “thread” in Japanese.
I decided to use スレッド to refer to “thread” and スレ for “post” (ポスト refers to mail so it felt weird to use). This might be something that might need clarifying and be added to the guide for future reference.
Edit: If there’s only one style you know how to write and all this talk about Keigo is above your current level of understanding, then don’t worry about it. Just write what you can because any sort of production is better than nothing at all.