You can't simply reduce it to the container(that's what mkv, avi, mp4 are), it's a lot more complex than that. You could have the exact same video and audio in all of these and if you wanted, you could even put the ISO in them without re-encoding it.
In encoding, there is no best(on a popular forum about it, it's actually against the rule to use that word when asking a question), it always depends on a multitude of factors. Someone could make the worst 60fps video you've ever seen if he doesn't know or care about what he's doing.
But to make things simple, here's a couple things you can look for:
mkv and mp4 are both very good containers with a lot of interesting features. mkv has more features than mp4, but mp4 is more widely supported. With that said, if you don't use the extra features, they're mostly the same as other containers so it depends on what you do with them.
For the video codec, what you want is usually the most recent one that's considered ready for production which would be h.264(x264 being the most well know encoding software for it). h.265 is more recent but it's not considered quite ready yet. It's also pretty much the same for VP8 and VP9(you'll see those in wmv files), but VP9 seems to be more mature than h.265 so it's probably be a good option, even though the settings used for those are usually of lower quality since they require a ton more of CPU power to encode(but wmv aren't usually encoded with care so the result is often not so great).
Even with a good video codec, there's tons of settings you can use that can make it go from horrible to great and the bitrate/file size is often a poor indicator of quality since the faster you encode something, the bigger the file size and the lower the quality is while the slowest you go(usually), the smaller the file size and the higher the quality is but you can't really know the speed at which the encoder made the rip.
As for 60fps vs 30fps, it depends on the source. You need an interlaced video to make a good 60fps rip which isn't a problem if you have an actual DVD or BluRay disc since pretty much all JAV and IV are in the interlaced format. If the source is a digital download though, it will likely be progressive and you can't make a 60fps rip without interpolating whole frames which doesn't produce a very good result at all(it might work decently for some simple anime, but that's pretty much it).
Sometimes, even if you have an interlaced disc as source, the way the video was shot could produce problems like frames being in the wrong order(2,1,4,3,6,5 instead of 1,2,3,4,5,6 for example) in some part of the video so you'd be better off with a 30fps rip unless the encoder fixed this and other times the result will be 2 frames nearly identical next to each other for the whole video so you have pretty much the same result as a 30 fps rip but it takes more space.
Your best bet is to look for something ripped using MeguIV(it) or an encoder who uses QTGMC on his own as the deinterlacer(other than vitreous and me, I don't know of anyone else here though), whatever the format is since that's what will look best most of the time.
And for a simple answer, I'm personally a fan of mkv with an h.264 video.