I’m a little obsessive about this myself.

Usually I have

• Dark colours, woolens, and delicates
• Stuff I think could run (raw denim, etc)
• Whites
• Light colours and stuff I don’t care about fading, which can be washed either way.

While most non-colour detergents don’t contain bleach any more, they contain optical brighteners that absorb UV and emit white light, to make whites look “whiter than white”. This can make dark colours, and especially blacks, look dull grey. Other than that you don’t usually have to worry about most colours, especially after the first wash. There are exceptions to this, such as raw denim which runs like crazy. You can also get “colour catcher” sheets for peace of mind that stop runs.

Usually I use a non-biological delicates wool detergent for dark colours, woolens, and delicates, which I wash together, on a wool cycle. It doesn’t hurt to wash something more delicately than it’s supposed to be washed, and it means I don’t need to do as many loads. Sometimes I’ll throw light colours in with this if I have room. Anything “runny” I’ll wash with like colours, at least for the first few washes.

Whites, light colours, and stuff I don’t care about looking dull like towels gets the cheapest own brand biological detergent.

If you have dark coloured bedding you may want to get biological colour detergent, I don’t.