CC + Wireless Connection can support massive libraries. There is at least one user with a CC library larger than 40,000 books, and many people have libraries in CC larger than 10,000 books. A 200-book library is minuscule. NB: with a large library you should take a look at our FAQ
[Android] I have added a lot of books and now adding books takes forever. What do I do?. The suggestions in that FAQ are especially relevant to CC libraries on SD cards.
Assuming that for some reason the wireless device isn't for you, another possibility is the CC Cloud Local Library connection. You put a full copy of your calibre library onto an SD Card, perhaps using a card reader, then use CC to browse that library to get books you want to read. Our FAQ
[Android] I have a copy of a calibre library on an SD card. Can CC use it? might help.
CC does not support upwards-synchronization of books; auto-uploading of changed books to calibre. It does support downward sync; auto-downloading changed books from calibre via the wireless connection.
As for the question about Dropbox speed, I suggest that you try it. Performance strongly depends on your network speed, so no one can tell you in advance what yours will be.
As for the rest, I leave it to others. I am not going to spend much time working out ways for you to avoid using my product.