Lightning and Water are the only 2 that don't mix. That is where I got stuck. And I'm going to make a guess of the number of Air Dragons you have at about 12. So you need.
18 Earth
23 Lightning
31 Water
34 cold
38 Air
The great thing about air is that it breeds with all of them with an 8 hour rate (apart from the sandstorm, but we won't mention that **cough cough**). So optimal breeding to not double up ... You have 144 elements required, so 72 dragons is the minimum you will need to breed to have them all covered. You have 72 spots available in your HC? Like you say, let's start with half an half Mud and Quake. Quakes are better earners, but if you're just breeding them to put in the HC it doesn't really matter.
9 Quake - 6 hours
9 Mud - 6 hours
That will complete your Earth shrine and leave you with
14 Lightning
22 Water
34 cold
38 Air
14 Storms - 5 hours
This will finish off your Lightning shrine and leave you with
22 Water
20 Cold
38 Air
16 Snow - 8 hours
This will even up your numbers to
22 Water
4 Cold
22 Air
2 Ice/Iceberg
2 (more) snow
20 Fog
You can adjust these last breeding numbers when you get your Air Shrine and you know where you are, but the optimal breeding strategy (until a new multi element hybrid is released, lol) is
9 Quake - 6 hours
9 Mud - 6 hours - Earth is complete
14 Storms - 5 hours - Lightning is Complete
18 Snow - 8 hours
2 Ice/Iceberg - 8 hours - Cold is complete
20 Fog - 8 hours - Air/Water are complete
That makes 72 dragons. Hope that helps.