The structure does indeed have a very small impact. Specifically access to a couple very specific rituals or styles, such as smokeleaf circle or christian style. You might want to look at the wiki when choosing your structure to see which options enable which small features.
For the precepts, its important which ones are required and which are forbidden. Especially if you are planning to mix and match. The grey/white/yellow coloring indicates how far away it is from "baseline" gameplay. Grey coloring is fairly similar to vanilla, non-ideoligion gameplay....blinding is abhorrent, so is cannibalism. Clothing required is lower and torso for women, and lower for men. Marriage is 1 spouse only. I'm pretty sure all the "who takes who's name in marriage" options are grey, because they have almost no impact. White options are a significant step away from vanilla gameplay. cannibalism acceptable, for example. Or many "preferred" or "disapproved" options because its a small mood penalty or bonus. Yellow are significant changes. Cannibalism required (ravenous) or scarring (extreme) or raiding (required) or slavery (honorable). I'm pretty sure that the "chance to have [precept]" in each meme is mainly for the computer generation of the NPC/AI ideologies. They might have that precept, or maybe not.
You can absolutely change all of the precepts...within limits. You can't remove a required precept. You can't add a prohibited precept. Some precept options are locked to certain memes. Ranching (Central) is locked to the Rancher meme, for example. Nutrient Paste (don't care) is locked to the Technology, bodder-modder-ish meme. Insect Meat (delicious) is locked to underground meme. The "Add precept" button at the top of the precepts icons is ABSOLUTELY worth taking a look at. You can see which memes are available to add an easier or harder/stricter gameplay experience, or to add give-and-take precepts....for example the bigotry (intense) precept makes everyone upset if you have a colonist of a different ideology, and a big social penalty with followers of different ideos, but if all your colonists are the same ideo (the one with that precept), you get a permanent +3 mood boost. Note that mousing over a precept that is "active" will tell you what it does (what moodlets it gives, what it prohibits, etc.), but the name of the precept will usually only give you a general idea. So mess with those precepts and read those tooltips to see the specifics and make sure you get what you want. Trees (desired) obviously implies that you want to live in a forest...but you need to select and apply the actual precept (which requires a certain meme I believe) in order to see that for the most part, its meant as a large penalty for few trees, and only a tiny boost for tons of trees!
I'm not sure what culture does exactly.
Some general tips.
1) don't build a fixed ideology. Not until you're REALLY comfortable with the system. You can't change it if you make a tiny mistake.
2) Instead build a fluid Ideology. You're limited to picking only 1 meme (to start), but you can still select ALL of the precepts you want (except the ones gated behind a meme you intend to add but haven't started with). Every time you reform the Ideology, you can add or remove a meme, or add or remove a style, and THEN you can edit all your precepts/apparel/rituals/roles/etc. EVERY TIME you reform. So you find out you don't really like something you picked, or it doesn't work the way you thought? No problem, its a new, tiny ideoligion! I'm sure no one will mind a little flexibility!
3) on the topic of reforming. Reforming requires development points. Development points are gained from good or great rituals or converting people. So...make sure you can get them. When you make an Ideology, you should add a large amount of rituals, able to be performed at any time. This means you can do a skylantern festival for 1-2 points, and then follow it up a day later with a social gathering, and then a dance party. 2 days later have a DIFFERENT social gathering. Also its not a bad idea if your resources allow, to capture raiders, convert them, and then release (or kill, or make an immobile bloodbag, I won't judge), since each conversion is 1 point. It takes 10 development points to reform the first time, 12 the second, 14 the third, etc. You can't save up for multiple reforms at once....if you have 16 points or 30 points or 10 points and do your first reform, you reset to 0 no matter what.
So, In short. Go for Fluid instead of fixed. Cherry pick the changes to all your precepts to what you want. Add precepts that aren't listed to get the ideo to where you want it. Have lots of rituals. Experiment with different things and use reform to change what doesn't work for you (or just save before reforming and mess around!)
For the precepts, its important which ones are required and which are forbidden. Especially if you are planning to mix and match. The grey/white/yellow coloring indicates how far away it is from "baseline" gameplay. Grey coloring is fairly similar to vanilla, non-ideoligion gameplay....blinding is abhorrent, so is cannibalism. Clothing required is lower and torso for women, and lower for men. Marriage is 1 spouse only. I'm pretty sure all the "who takes who's name in marriage" options are grey, because they have almost no impact. White options are a significant step away from vanilla gameplay. cannibalism acceptable, for example. Or many "preferred" or "disapproved" options because its a small mood penalty or bonus. Yellow are significant changes. Cannibalism required (ravenous) or scarring (extreme) or raiding (required) or slavery (honorable). I'm pretty sure that the "chance to have [precept]" in each meme is mainly for the computer generation of the NPC/AI ideologies. They might have that precept, or maybe not.
You can absolutely change all of the precepts...within limits. You can't remove a required precept. You can't add a prohibited precept. Some precept options are locked to certain memes. Ranching (Central) is locked to the Rancher meme, for example. Nutrient Paste (don't care) is locked to the Technology, bodder-modder-ish meme. Insect Meat (delicious) is locked to underground meme. The "Add precept" button at the top of the precepts icons is ABSOLUTELY worth taking a look at. You can see which memes are available to add an easier or harder/stricter gameplay experience, or to add give-and-take precepts....for example the bigotry (intense) precept makes everyone upset if you have a colonist of a different ideology, and a big social penalty with followers of different ideos, but if all your colonists are the same ideo (the one with that precept), you get a permanent +3 mood boost. Note that mousing over a precept that is "active" will tell you what it does (what moodlets it gives, what it prohibits, etc.), but the name of the precept will usually only give you a general idea. So mess with those precepts and read those tooltips to see the specifics and make sure you get what you want. Trees (desired) obviously implies that you want to live in a forest...but you need to select and apply the actual precept (which requires a certain meme I believe) in order to see that for the most part, its meant as a large penalty for few trees, and only a tiny boost for tons of trees!
I'm not sure what culture does exactly.
Some general tips.
1) don't build a fixed ideology. Not until you're REALLY comfortable with the system. You can't change it if you make a tiny mistake.
2) Instead build a fluid Ideology. You're limited to picking only 1 meme (to start), but you can still select ALL of the precepts you want (except the ones gated behind a meme you intend to add but haven't started with). Every time you reform the Ideology, you can add or remove a meme, or add or remove a style, and THEN you can edit all your precepts/apparel/rituals/roles/etc. EVERY TIME you reform. So you find out you don't really like something you picked, or it doesn't work the way you thought? No problem, its a new, tiny ideoligion! I'm sure no one will mind a little flexibility!
3) on the topic of reforming. Reforming requires development points. Development points are gained from good or great rituals or converting people. So...make sure you can get them. When you make an Ideology, you should add a large amount of rituals, able to be performed at any time. This means you can do a skylantern festival for 1-2 points, and then follow it up a day later with a social gathering, and then a dance party. 2 days later have a DIFFERENT social gathering. Also its not a bad idea if your resources allow, to capture raiders, convert them, and then release (or kill, or make an immobile bloodbag, I won't judge), since each conversion is 1 point. It takes 10 development points to reform the first time, 12 the second, 14 the third, etc. You can't save up for multiple reforms at once....if you have 16 points or 30 points or 10 points and do your first reform, you reset to 0 no matter what.
So, In short. Go for Fluid instead of fixed. Cherry pick the changes to all your precepts to what you want. Add precepts that aren't listed to get the ideo to where you want it. Have lots of rituals. Experiment with different things and use reform to change what doesn't work for you (or just save before reforming and mess around!)