Do I need to see the other two to fully appreciate this one?

"Red" stands on its own and you can watch it without having seen the other two films in the trilogy.

Of course, if you have seen them you'll enjoy the references made to them (in the conclusion of "Red"), but no - I don't think viewing them is a necessity.

As stated, not necessary really.

There's only one relevant moment where references are made to the other 2 movies, and that moment is not that interesting in the first place.

No. I think you could watch them in any order. I like Red best, though, so ending with Red might be a high note. Then again, maybe you'll like a different one better.