My strategy varies by how well I'm playing (or how well I think I'm going to play).
If I'm on my "A" game:
Start as Grey Joy. Light and defeat Martell. Light and defeat Tyrell. Start BW MB and bring Lannister into it (should be lit by this time). I typically save my Martel action button at this point (unless I know for sure I won't beat Lannister), MB usually completes Lannister. Make sure I don't multi-drain, and then go for HOTK. Saving the Martel action button allows for longer HOTK MB and bigger shot at much bigger points. I should probably bring Targaryen into HOTK instead, but that shot is so dang risky that I avoid it until after HOTK if possible, unless I just happen to have it dialed in. After that I grind out Targaryen coupled with lighting my MBs. It's important to get the easy dragons out of the way and bring the big boy in with a MB. Playing on an LE/Premium is especially helpful as the upper playfield really helps mode progression. Then you are onto the Iron Throne, and that, well, that is just plain good old fashioned super fun.
If I'm on my "B" game:
Start as Tyrell. Light but don't start Greyjoy (right orbit backhands are easy and low risk). Light Stark (backhanding that right ramp is so easy and such low risk) and bring Stark in with Tyrell. I focus on building Stark as much as possible and then cashing out with a little time left on Tyrell. Bang away at Tyrell and try to complete and get your locks ready for BW MB. I find it important to make sure you time out your mode before starting BW MB. At that point, I hit center ramp, bring in Grey Joy and Lannister into BW MB. The shots for BW MB line up so nicely with Grey Joy I beat the mode almost every time I play the MB. Plus, with the MB having balls flying around I typically light all my Lannister shots off of the risky stand ups and complete that mode as well. After that it's onto HOTK and basically my strategy above.
If I'm on my "C" game:
Start as Martell (if I'm playing shitty I like to be able to extend my MBs early and often) but I NEVER play Martel until after HOTK if I start as Martell. From here I follow the same strategy as "B." except it's a little more tricky/tedious because lighting Tyrell and not starting BW MB can be tough.
My grand champ score is right around 30 Billion the last time I looked going with these strategies (my top scores are all pretty well spread across those three houses). I find the most important thing is just to not blow the MBs. Focus on those and getting to the super jackpots and whatever you do, keep those shot multipliers and playfield multipliers running!
In any case, I hope that helps a few people that are stuck in the "there's only one house worth playing, and that's Martell" attitude. Branch out, figure out your play style and find the right house that builds on those strengths...
Last word of wisdom? is to practice, practice, practice the battering ram shot from a right flipper cradle. Once I gained confidence in that shot and the recovery my scores starting doubling.