There is no set of rules that will get a mod featured. At the end of the day, I generally look through the most liked, most downloaded and highest rated mods from that day and try to feature some that represent each category of the site. I'll go through some concerns I usually get:
"My mod has X likes and that featured mod has fewer, but mine wasn't featured!"
I look at more than just likes, and I look at them within a one day period. Sure a mod from a month ago will have 50+ likes and the one from today might have 10, but the rate at which it gained likes was higher, and I usually only feature files from the past day or two. Also if all four of the top liked mods from the day are vehicles, I generally don't feature all four.
Community interaction on what gets featured
I never really understand this request - the featured mods are already decided by the community. They are based off downloads, likes, comments and ratings, all things that require the community to interact with a mod. Do you really want yet another mechanism for voting? I don't think that's the solution. The only thing missing here is an automatic trigger that features something when it gets to a certain like + download count. And this is a favor to everyone who isn't a vehicle modder - you probably wouldn't get featured without admin intervention because vehicle mods generally dominate in terms of likes and downloads.
That all said, I will admit that I used to not be good about this, and a lot of great mods in the past went unfeatured. I'm trying to make up for this by featuring them now when they get updated with new versions.