The Notes app posts to whatever default account you have set in Settings > Notes. I suppose if there is no default account, it might ask for the account. I've never encountered that.
There is no way to create a note in a folder. The note will always be created in the top level All folder for that account.
The easiest way to move notes later is to make sure you have Notes set to sort by Date Created, or Date Edited. That way recent notes are always at the top and easy to find. I prefer Date Edited, since that keeps notes I'm actively using near the top. You set this in Settings > Notes.
I really wish Apple would let you change the sort order in the Notes app instead of going to Settings, but that's how it is for now.
If you want more powerful note taking, arrainging, and searching options, there are many other note apps. I use Notes because my needs aren't all that complicated; also because I rather like the drawing mode and the way it saves links.
Note note: The note creation dialog gives you the option of creating a new note, or adding to the end of an already existing note. There is no folder option. I'd like this option as well, but have been unable to find one, even using thrid party apps. We'll have to wait for Apple to add the option, or use a different note app.