There's a horde of math below to explain why, but if you just want to start off with a fairly optimal layout, just recreate this:

• Our objective is to progress as quickly as possible towards unlocking the whole farm. This means maximizing Spare Part generation
  
• It seems to me that the biofuel is what yields the most money. Therefore I'm going to assume that maximizing biofuel production is the goal for maximum progression.
  
• All calculations are based on Cauliflower, Potato and Turnip. That said, all calculations scale linearly so it's easy to adjust for other crops (e.g. more/less water, faster/slower growth)

Biofuel Converter:
- 18 seconds to complete

Bots:
- Movement of ~1 square per second
- Charging takes 15 seconds (Biofuel Bot)

Biofuel Bot:
- 4 actions before charge

Water Bot:
- 4 waterings before getting more water
- 20 waterings before recharging
- Refilling water takes 1.5 seconds
- ~1 second per action watering

Harvest Bot:
- 6 harvest per charge
- ~1 second per harvest

Assuming storage and bots placed next to converter, there would be on average ~6 movements per placed item. The placements are immediate and so are the pickups. This means each placed item takes 6 seconds, and a total of 18 seconds to start a converter.
The bots do four actions before charging. Hence, one Biofuel Bot can cover 4/3 of a Biofuel Converter.

Conclusion: 3 Biofuel Bots per every 4 Biofuel Converter

This of course will depend on which crops are being used. I'm going to assume that Cauliflower, Potato and Turnip are being used, or put different that crops with a completion time of 300 seconds are being used.

At perfect efficiency, the Biofuel Converter can complete in 18 seconds. Practically though, with only one Biofuel Bot, it will take 6 movements X 3 items to reload it, or another 18 seconds. In addition, the Biofuel Bot will sometimes charge at suboptimal times. Therefore, in practice, the Biofuel Converter is likely to take more than 36 seconds to complete a cycle. I'm going to assume 40 seconds to complete a cycle.

Conclusion: We need 3*300/40 = 22.5 patches per biofuel converter (for 5 min crops, adjust linearly for faster/slower crops)

A watering bot if perfectly optimized can water one crop and move to the next crop in 1+1 seconds. I'm going to assume 3 seconds per watered plant though as there will be some suboptimal movements
On a full charge (20 waterings) this means 20*3=60 seconds on watering movements. It also means 5 refilling of waters, that takes 1.5 seconds each and I will assume 5+5 movement per each refiling. This means 5*(1.5+5+5) = 57.5 seconds spent on refilling water. Then another 5+5 movement assumed to go to the recharging place. This would bring a total time per full charge of 60+57.5+10 = 127.5 seconds.
During a full charge, the bot will be watering 20 plants. A Water bot waters 20 plants in 127.5 seconds, or 6.375 seconds per plant.

Just like above, I'm going to assume that we are planting Cauliflower, Potato and Turnip. Cauliflower needs 7 waterings per 4:50, or 41s per watering. Potato needs 5 waterings per 5:10 or 62s per watering. Turnip needs 4 for 5:24, or 81s per watering. On average, this means ~61 seconds per watering. I'm going to assume this average.

Conclusion: A Water Bot waters one plant every 6.375 seconds. A patch needs to be watered every 61 seconds. This means a single bot can cover 61/6.375 = 9.6 patches (assuming 61s watering plants, scale linearly for higher/lower values)

The harvester needs to move back to storage after each harvest. Let's assume on average the distance for this is 5 squares, then movement would take 5+5=10 seconds per harvest. Plus 1 second for the actual harvest. Dropping off is instant. There are 6 harvests per charge, or a total time of 11*6=66 seconds. Plus another 15 seconds for charging. This means a total time per charge of 81 seconds for 6 harvests. Or, 81/6=13.5 seconds per harvest.

Just like above, I'm going to assume that we are planting Cauliflower, Potato and Turnip. They have roughly a completion cycle of 300 seconds.

Conclusion: A harvester can cover 300/13.5 = 22 patches (assuming ~5 min crops, scale linearly for other crops)

To summarize ratios:
- 1 Water Bot per ~10 patches
- 1 Harvester Bot per ~22 patches
- 0.75 Biofuel Bot per Biofuel Converter
- 1 Biofuel Converter per ~23 patches

It looks like a reasonable design could involve
- * 20x Crop Patch
- 2x Water Bot
- * 1x Harvester Bot
- * 1x Biofuel Bot
- * 1x Biofuel Converter
- * 1x Storage Unit
- 1x Water Well

One possible layout for this is (5-minute crops):


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Later in the game, if using ~8 minute crops, the following is one possible layout (with updated ratios):

If you want to contribute, please contact me and I'll add you as a contributor to give you edit rights