Dogs in the Vineyard is a great game. It really demands that you play it by the rules as written, which may be a cognitive leap if you are used to fudging things. I think the rules are luminously clear, but they are pretty specific and work great when you do what they say. If you don't the game suffers.
I would strongly suggest playing it straight the first time. Adding the burden of hacking things to play Jedi or whatever is only going to make it that much harder to work with. Once everybody "gets it", by all means experiment. A cool way to pitch it: "Dogs is about these kids who are told to go into their communities and solve serious problems and the tools they are given to solve the community's problems are a book and a gun."
As GM, make a town you find compelling and go all the way to hate and murder. Don't forget to ask the players if they are seeing demonic influence, and add those fat dice to your collection when they do. Don't be afraid to play hard, even really hard. The players have the resources to deal with it. Do not nerf your opposition, make them full of power and danger and strong motivations.
Leave a few relationships you can directly slot in as important to specific PCs. Be prepared to say "this guy is your older brother" and "This girl? She's the first girl you ever kissed, which I see you wrote down as a relationship" or whatever is going to resonate with the relationships they have chosen.
Don't keep secrets. Seriously, don't! As GM be an open book. It is not only acceptable but required to say stuff like "She shakes her head and denies any knowledge of the theft. And she's totally lying" or "Youpass by, and as soon as you are out of sight all three brothers spit in the tracks you left with contempt". No secrets!
Understand that even three Dogs acting in unison are generally unstoppable. Make sure your town has enough moral grey areas to divide them against each other when it comes time to make solutions, or have another town ready to go because they will breeze through the first one. This isn't a terrible thing, but the game is much better when you get some player-level disagreements going. When one guy is like "Hell no, you aren't making him Steward!" that is good stuff.
Really use the initiation conflicts to familiarize yourselves with the way escalation works. Remember that you can escalate from guns to talking, and that you take harm in relation to the action, not the level of escalation.
Encourage giving! This may be the biggest thing I see among people new to the game. In a lot of games, you have to fight to the bitter end. If you do that in Dogs, not only do you lose certain rewards from fallout, but the game can be boring. Give! Set stakes that allow easy giving and encourage it.
Like it says, Roll the dice or say yes. If it isn't worth a conflict, let it happen. Pick your battles as GM, and be OK with losing, because you definitely will.
Don't sweat the dice. If a guy takes "Gnarled fists 3d10" that is awesome, not problematic. He wants to punch people and be a badass, and he will be. It will not break the game in any way. Similarly, players will come to relish fallout and that is fantastic. Let them get banged up and learn from it and get better. Failure is OK.
Remember the faith is what the players say it is. If anyone is weirded out by the setting, make sure they know they can quite literally change it. They are God's representatives on earth. If he tells them polygamy is no longer cool, it is no longer cool. That's the stuff of great conflicts. If this is sufficiently clear, it will hopefully remove any discomfort about the setting.
Here is a thread with even more advice! Good luck and have fun!