Marjorie was extremely popular in the 1920s, and has always been the more popular spelling in the United States (well, since the 1880s at least). I prefer
Marjorie, and it seems fresher and younger to me.
Margery is fine too, but it looks more medieval. Margorie looks weird; I've never seen that spelling before.
Margery /
Marjorie is usable in a modern context. It's not any more "old lady" than
Alice and
Eleanor and other names rising in popularity.
http://www.behindthename.com/top/search.php?terms=margery+marjorie
Marjorie,
Dorothy,
VirginiaMargery,
Amabel,
Lettice
That's the feeling I get from the different spellings.