Can I control which DNS record a client application uses?

Can I control which DNS record a client application uses?

I'm trying to make our set of servers more fault tolerant. I have a web
server, a mail server and a PBX server that uses SIP. I know that for each
service, I can have the DNS return multiple A, MX and SRV records
respectively. However I'm not sure if the DNS will indicate which record
the client should use first or second.
For instance, if my primary mail server is reachable, I want mail clients
to always connect to that one and never the back up. Like wise, if the
primary is unreachable, I want the client to then try the back up.
I know that their are other ways to implement fault tolerance (I'm looking
into them), but I want to know specifically if DNS resolution will work
this way.