Ok, so you got your skill list and your resolution. Time to ask yourself another thing: what do the players do in this game (and the possible corolary: what does the GM do?). Is there even a GM? Are the players trying to overcome the challenges of the GM and the GM is setting up challenging situations? Are the players pursuing the individual motivations of their characters and the GM is setting conflicts around those motivations? Are the players trying to live out their dream of the wild west and the GM is directing the dream? Something else?
Now this is another of those things where if you don't have an idea about what the players will be doing - if everyone at the table doesn't have an idea what they'll be doing - you are having a problem. But you started with an idea for a game so it's alright, yeah? Thing is, that focused our game and allowed it to run and not flounder, but it didn't (yet) make it more flavorful or sustainable.
There's two things left to do: subsystems & currency.
This is a wild west game so there are probably going to be shootouts and maybe we need some extra rules for that*. We create extra rules for any part of the game(play) that we think needs zooming on. These are our subsystems. The various discrete groupings of rules that handle how more specific things should work out.
Much as with the initial skill list, we look to our source material to see how things should work. We also look at our life experience and our outlook on things. Maybe you think that gambling corrupts people, and make some gambling rules that will suggest that. Maybe the source material supports that or maybe we're mixing it up. Last but not least we need to look at the social level, the actual people at the table, and our question about what they are doing there. If we initially said that this was a game of overcoming challenges but our rules make it so that one player is seriously gimped in contrast to another in solving those challenges, then that's probably no fun. How is it working at the table, for us, as people, is it pressing the right buttons, occupying or provoking us in the right ways?
All this time we need to take steps back and see how things interact. How (sub)systems trade between each other, how a change here influences some consequence there. If I shoot you with my revolver, how many health points does that subtract? What does the source material say about it? What does our outlook say about it? How will it impact the dynamics of the people at the table?
If I'm shot, can I spend Grit points to survive? How do I earn Grit points? If Grit points make me survive, then what kind of man survives long in the wild west, in this game we're making. If you earn Grit by shooting people, that means that the more people you shoot, the longer you'll survive. Is that something we want our game to say? What if our source material and our moral judgement says "live by the gun, die by the gun"? How do we make the game say that? This trading between parts of the system, this "what is our game saying", this emergent effects that come from parts of the system interacting is where the real work of design comes in and often flounders.
Take the Pathfinder Cavalier class. It has a lvl1 ability called Challenge. When you make a challenge to an enemy, you get a bonus to damage against it and a -2 to AC except that enemy (plus another benefit usually vs the challenged enemy, depending on the cavalier's order). Now, from where I stand, that has two effects:
1. if I am the challenged monster, I want to get away from the Cavalier
2. if I am a monster not challenged by the Cavalier, I want to attack the Cavalier.
So what the game is saying there (in an exaggerated manner) is: "when the Cavalier challenges an enemy the enemy runs away while other enemies swarm her". Is that what the designers wanted it to say? I don't know, maybe. Anyway, that's where design happens.
Going really quickly back to that "gambling corrupts people" thought. One thing you could do (but maybe not the best) is this:
1. make it almost impossible to win at gambling (like real life)
2. give the player the option to use some special resource (like cheating) to dramatically increase their odds
3. 1+2 = temptation
4. using up or amassing that resource ("cheater points") interacts with some other part of the game that indicates the character's corruption and creates incentives for bad behavior and/or more gambling and so on in a circle or down a chain of consequences
Now, the bits I covered in Part 1 can really be done in 5 minutes. Part 2 can take days, weeks, months or years, often with going all the way back to Part 1 and starting from zero. Sometimes you never make it work. Trashing stuff is always a huge part of the process. But if you've got a really clear idea of what you want your game to do you can have both Part 1 and Part 2 done in minutes ready to play and then you flesh it out or junk it later. So if you've ever wanted to design a game but didn't know how, try this. There are other methods of course and the one I just proposed will definitely not result in some original and groundbreaking game that everyone will take to like fire (you won't get Fiasco this way for example). But it will be your little game that will do the things you want when you want to do that specific something. It's really the same as houseruling an existing game to make it behave the way you want except you're starting without any assumptions.
*Personally I've now been long tempted to make a game that features combat but no combat or health mechanics. Well, I actually have made it but never tested.