I want to have a simple WYSIWYG when people add comments and when people edit the body of a basic page.
Something that looks like this:
I used ckEditor, it works fine.
You can also install wysiwyg which manage many wysiwyg editor like ckeditor and others. You can try simple editor too.
You can install the WYSIWYG module. This will allows you to install severals other WYSIWYG, like CKEditor, TinyMCE, etc..
Once you've done it, you can create a new filter format and a new profile with your settings (so you can show only the buttons you want). The you just have to set that format into the fields. For that I think Better Format module will help you.