Simplest would be a conductivity measure, as it tells the ions in the water and is simple to do. A turbidity cell ( either transmissive, reflective or both) will tell you about suspended solids. For oxygen you are going to have to bend over and buy a commercial sensor cell, as they are not really DIY items, they are basically an electrochemical cell made to fine tolerances. Easiest is to use a trickle tower ( which is very easy to DIY with a big piece of plastic drain pipe and a whole pile of plastic shapes like reject mouldings and a blower at the bottom or a catch tank and a spacer) to ensure oxygenation is good, and place this in a shaded place where it will not get hot. You might want 2 so you can strip and clean the one while keeping flow going.
Good design is a lot better than fancy monitoring, and as you will have a planted area to dispose of nitrates easily it will be better to have a bypass to let the water get filtered through the plants as fertiliser.