• Farms should be your main food production. They have both the best yield per worker, and better yield per in-dome space than hydroponics.
  
  If you don't want to look the best up: Combine Soybeans with Potatoes. With later techs, replace Soy with Fruit Trees, and (Giant) Potatoes with (Giant) Corn.
  
  
  
• Hydroponic's Microgreens have decent yield per water, though farms get better at that later on. And Algae is the best for oxygen - just need one worker to produce 1 oxygen in a 3-hex building.
  
  
  
• Fungal Farms actually cost oxygen, and have low yield. However, they have the best yield per water (until you get techs and spires to reduce a dome's water usage).
  
  They also serve as a decent failsafe: They don't require in-dome space, only need 1 metal as maintenance, and their food-production is instant - just have them sit idle outside of your domes, and if you find yourself too low on food you can get some (inefficient) food-production right away, to keep you alive until the farms do.

• Normal Ranches are a viable alternative for main food production. Their yield per sol is slightly worse than a farm's without additional crop-types, but ranches do not require botanists, don't need to worry about soil quality, and have better yield per water. In fact, they beat even fungal farms in water-efficiency (except when using geese).
  
  However, with Gene Adaption and/or Giant Crops farms offer significantly greater yield per sol, making ranches worse for late game. Though they still have an advantage for yield per water.
  
  
  
• Outside Ranches are another alternative for main food production. They have better yield per worker than ranches and farms without Gene Adaption/Giant Crops. However, they have worse yield per water than ranches and some farm crops, and worse yield per oxygen than ranches.

I did the maths here: https://docs.google.com/spreadsheets/d/1EbnziHMz9baojTDnFQD2J5DInztB00iq0dV-R2qtgP8/edit#gid=0
Info on hydroponic and fungal farms in the other tabs. Now includes stats for ranches and open farms. Includes more stats than what I posted here.

This assumes yield scales linearly with performance (which is highly likely, but I've never actually seen it confirmed anywhere).

Soil quality affects work performance linearly - no change at 50% quality, -50 at 0, +50 at 100. With other words, if your workers have 150 performance, you can get up to 200 total with maxed soil quality.

Crop failures not taken into account for the maths, not quite sure how they work (and you really didn't minmax things if that happens).

Per Sol and worker: Farms are the way to go. Hydroponic and fungal are equal at first, but hydroponic beats fungal once you get better crops. Fungal farms can keep a slight advantage if you get the Superfungus breakthrough.

Hydroponic: Utility crops do not help here.

Farm: Cover Crops + 4x [Crop Type] would require micromanagement. Best micromanagement-free alternative is given as well.

If in-dome space is the limiting factor, farms still beat hydroponics. But fungal farms don't require in-dome space at all.

Fungal farms are surprisingly good here. No crop-type and crop-rotation beats the fungal farm's yield per water, up until you get the "Water Conservation System" tech, or place a "Water Reclamation System" spire.

The hydroponic farm is kinda boring, when it comes to water: Microgreens have the best yield per water, and don't require any techs.

Farms: Utlity Crops does not help with water-efficiency.

You need just one worker in a (hydroponic) farm to produce oxygen. Workplace performance does not seem to matter at all for this. (Note that there's currently a bug that sometimes causes Hydroponics to produce oxygen, even after being disabled or destroyed)

Farms only have one crop that produces above-average amounts of oxygen: Fruit Trees.

Hydroponics are better if you don't care about yield: Algae produces the same amount of oxygen as Fruit Trees, Kelp half that. Both with 30% the hexes required, and less water needed. The yield per Sol is significantly worse, however, but hydroponic farms are still an option if you need a dome to run without oxygen for a while.

Fungal farms actually consume oxygen. Definitely not a good idea if you're running low on air.