All microbes will have a different neural net that will change itself depending on the physiology of the microbe. The only difference is that the player will be able to edit his auto-generated (so you could immediately play after adding a toxin vacuole and not fearing that other members of your species wouldn't use it) neural network. So I don't really see "two systems" as you called them.
Each player will have different neural networks. The weights and thresholds would change over time, but so would the topology. You would get extra inputs (when you evolve signal agents and stuff) and outputs (such as flagellum and toxin ejection).
The inputs would likely not be between 0 and 1; neither would be the firing thresholds and the outputs. We could obviously have a node that fires only one or zero, but a lot of the time we would love to have a logistic function, so you would output a higher number if the input was higher (for things like movement).
The species would have to decide which species was more of a threat/more of a food source. We'll be using logic gates and simple operations (which can all be formed using nodes, we just use this as an abstraction), so we could have a Max node with two inputs. The first input would be species1 (1 if present or 0 if not) multiplied by distance and weight of connection (say 3), while the second would be species2 (1 or 0) multiplied by distance and weight of the connection (say 5), so if this species1 and species2 are both the same distance away, the Max node will only relay the information for the second species (larger value) and the species will move accordingly.
Say both species 1 and species2 are predators, we wouldn't want to go away from species2 only to run in the opposite direction and hit species1. In this case, we would not use a Max node, and would blend both inputs to instead move in a direction that gets us as far away as possible from both. I have a prototype of this lying somewhere...
Does this make sense? I'll try to draw up the neural networks for all the species we have so far, so it is easier to implement (and then we could actually move onto evolving/modifying them).