For 2FA I'd suggest that you use Authy. It works across multiple devices and unlike Google Authenticator it allows you to make a backup so that when you change phones you can restore all of your accounts used with Authy.
DST doesn't affect the underlying time in GMT/UTC. It just adjust the relative time around that. So no DST issues (as long as it's done properly -- it should generally happen automatically based on the selected server time zone).