To craft higher level potions as you level up, you need to increase the first passive to use higher level solvents.

To craft more powerful end-game potions with multiple effects, you'll want to put points in the passive that lets you use three ingredients.

To make those endgame potions last longer, you'll want the passive that increases their duration.

If you want to harvest your own ingredients, keen eye is helpful for spotting reagents.

The passive that removed harmful effects is generally unnecessary.

Generally speaking, for leveling up the potions that drop from enemies should be sufficient. For end-game, I personally just buy the potions I want. Spellpower potions that give magicka, spell power, and spell crit tend to be good end game potions, made from lady's smock, cornflower and either water hyacinth or namiras rot. This might be a helpful source (for the recipe for spellpower pots): http://tamrieljournal.com/list-of-useful-potions-and-alchemy-reagents-in-eso/

I typically only use crafted potions in PVP, vet dungeons, trials, or arenas like VMA. For overland questing and normal dungeons, dropped magicka potions work fine.

Honestly, for the rest of them, it depends on whether you want to focus on leveling first and fill in the blanks later or you want to focus on crafting first.

If you focus on leveling, put skill points into the crafts you actually use as you level. Probably, clothing and woodworking for light armor and staffs as a sorc. Personally, I find that buying food or drinks (festival foods/drinks work great since they scale by level) and relying on dropped potions works fine for leveling.

If you want to focus on crafting, make sure you are getting all the standards in a zone or you will find up feeling starved for skillpoints. You can pick up all the passives you want.

Generally speaking for passives:

Keen eye is handy if you want to farm your own mats. Otherwise useless.

Hirelings are handy if you are okay with getting mail every day you log in with extra mats. Great if you have the crafting bag, otherwise gives me inventory management problems but can be a good way of getting various crafting mats.

The first passive will always raise the level of what you can craft as well as the level of found materials. Mats in the world scale, 50% from level, 50% from this passive.

Provisioning and enchanting have a passive allowing you to make stuff of higher quality, green, blue, purple and gold. Very important if you plan on crafting your own food/glyphs. If you don't, ignore this. I usually buy anything I want for food/drinks/glyphs.

Blacksmithing, Clothing, Woodworking and Jewelry have a passive that cuts the cost of upgrading to green, blue, purple, gold. Very important if you plan on crafting your own gear and upgrading it.

Blacksmithing, Clothing, Woodworking and Jewelry and Enchanting have a passive that increases the quality and quantity of mats you get from deconstructing gear and refining raw mats. This is very important if you are trying to collect crafting materials and upgrade materials. Its a good way to maximize your returns, especially for expensive crafts like Jewelry.

Alchemy has a passive allowing you to use 3 ingredients, very important if you plan on crafting your own end-game potions. I'd save this until you actually need to craft end game potions.

Provisioning and Alchemy have a passive creating more than one food, drink, potions or poison. Very important to cost effective crafting. If you are going to craft a lot of food, drinks, potions or do daily writs, grab this passive.

Provisioning and Alchemy have a passive increasing duration of effects. This is probably useless for food/drinks unless you are using psijic/mythic ambrosia, but very worth it for potions. I'd pick it up once you start using end-game potions for content where you get the most bang for your buck, or for drinks if you are leveling with psijic/mythic ambrosia.

Hope that helps a little with what passives are useful and why they are used.

Sunshine Daydream's Guide to Crafting will answer such questions as these, but you're asking for entirely too much information to rewrite in forum post(s). Whatever you decide to do, have fun out there!

edit: Also, this source is up-to-date unlike that 4-year-old link that was never updated even after poisons were introduced to the game and some traits changed... beware of relying on old/outdated information.