This is such a good question Loren!
Here other teachers will probably disagree with me, but in my experience the "up" here adds no meaning at all to "put." It can be a phrasal verb (e.g. to put someone up for the night = let them stay with you) but "put up" and "put" in your sentences are synonyms.
"Set" = place, whereas "set up" = construct, establish, assemble. So both can be used here, but the meaning is not identical.
The issue is that "up" can be added to many verbs without changing the meaning. This is a more casual way of speaking, though. For example, here in Canada, we might say "the sky cleared up after the storm" but this is exactly the same in meaning to "the sky cleared after the storm." Again, some teachers might want to "split hairs" over this one, but don't worry, all your sentences work :)