I agree with G. Moto and robort. I play a 3 color deck in competitive modern and I spend way to much time thinking about my mana base. I think the best way I can help is to pretend I'm the sliver player (assuming this is modern) and walk you through each choice in that mana base.
4
Mutavault - probably the best manland available in the format. being able to turn into a 2/2 for 1 mana is huge, and since the vault is all creature types, it gets the additioanl advantage of being a sliver and getting all the perks of the ther slivers. It's biggest downside is it makes colorless mana, and since slivers can be as many as 5 colors, being stuck with grey mana can be a problem.
4
Sliver Hive - Pretty self explanatory. A land that can be used for any color as long as it's for slivers and can spit out tokens. its an easy 4 of.
4
Cavern of Souls - Much like
Sliver Hive, as long as we name sliver,
Cavern of Souls gets us any color we want, and makes the slivers uncounterable to boot. This is especially good for slivers, since they tend to run a higher creature count than most decks.
4
Verdant Catacombs - Fetch lands are staples in Modern. They let us find whatever color we need. In this case, this fetch can find any of the lands remaining in the deck (
Godless Shrine,
Overgrown Tomb,
Watery Grave,
Blood Crypt,
Swamp,
Forest) because all of them are either a
swamp, or a
forest. this would let me find exactly what I need. For example, I have a red sliver and
Path to Exile in hand. I play
Verdant Catacombs and pass the turn. If my opponent plays a huge threat, I use the fetchland and find
Godless Shrine (pay the life to untap) and use Path. if my opponent does nothing, i fetch the
Blood Crypt (tapped) and play my red sliver on my next turn.
Remaining Non-basics - These were mentioned above, and are going to be distributed based on the number of each color card in your deck. In this case I'm guessing the deck is mostly green / black, since every land produces at least green or black. The other colors may be splashes for specific cards.
Basic Land - Basic land are more important than you might think in competitive formats. In Modern,
Path to Exile is a staple you can expect any white deck to run 4 of. Having at least a couple basic land to find means you aren't just letting your opponent
exile your creature for 1 mana. Same goes for
Ghost Quarter (which you might expect some people to sideboard in against you). The final (and most important) reason to run at least 1 basic is to play around
Blood Moon.
Blood Moon is very common competitively and this sliver deck is very susceptible to it. Having two basics means if
blood moon comes down, we may be able to play around it. As for why our basics are black and green, it probably has to do with
Gemhide Sliver, which would let us get around
Blood Moon entirely.
Blood moon also explains why (as you mentioned) red decks seem to be the only ones who use a lot of basics, because they don't care if they get hit with
blood moon and in many cases, they run it themselves. There are cards that shut down basic land (
Boil,
Choke,
Flashfires) so having too many can be
dangerous.
Other general tips when thinking about mana base.
1. Always coming into play tapped is a major disadvantage, and the land needs serious upside to makeup for it.
Shambling Vent is a good example. It always comes into play tapped, but once its untapped, you have access to 2 colors and the potential for a 2/3
lifelink.
Darkslick Shores is another good example. It can come into play tapped, but only if you have at least 3 land. And in a format as fast as Modern, knowing you can have one of 2 colors on turns 1, 2 or 3 from one of these land (or any in the so-called "lonely land" set) is major upside.
Well I hope you found this helpful and didn't mind reading my novel of a comment. Good luck and Happy Hunting
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