Changing the MX is easy. Configuring exim on the backup server (it doesn't have to be exim) to forward all email to the main server once the main server is up, is easy too.
If you have POP or IMAP running on the backup server you'll have email stored on both servers, not good for your clients. So your clients will probably be without the ability to receive email while the main server is down. If this doesn't work for you then you'll have to do what the big guys do, which is a high-availability cluster. Not controllable in any way by DA, and you're entirely on your own if this is what you want.
The hardest part (without that high-availability cluster) is letting the slave know who the valid accounts are on the main server, and keeping the list current, so if/when the main server is down, the slave still rejects mail for nonexistent users. Otherwise you'll have lots of undeliverable emails; what will you do with them? You can't return them because most of them will have forged senders, and you can't deliver them, and according to RFCs you can't just throw them away.
This topic has been discussed several times on these forums; each time I've pointed out that it's a lot harder than it looks.
Jeff