Aquatic insects can be a very good indicator of conditions in streams, and a favored one in good quality waters is the EPT index (mayflies, stoneflies, caddis flies) as intolerant species to pollution and low water quality.  But this index may not work in some low gradient systems with poor diversity of substrate, but each macroinvertegrate species has a pollution tolerance correlation and in some studies a rating can be achieved that may be helpful.  If you are unfamiliar with this, I have attached a link to a basic approach, and it may be helpful to find a collaborating aquatic microbiologist or seek an aquatic insect (macro-invertebrate) classification and identification manual if available for your area.  Aquatic insects are in stream full time, so if you go out to sample, you can generally find them.  If you sample water chemistry as an indicator, it can vary with time, or if sampling pollution, it can be episodic and you may sample a slug with high concentration or miss altogether.  My co-authored 1984 report on researchgate on Spruce Budworm Project used aquatic insects to help identify buffer success of pesticide application and effects of an accident and major spill.  

http://www.in.gov/idem/riverwatch/files/volunteer_monitoring_manual_chap_5.pdf

I would suggest to use the Trophic State Index by Carlson. You just need to measure the Secchi’s disc transparency, chlorophyll-a and phosphorus to describe the health of your ecosystem. The index defines a healthy ecosystem based on the biomass related productivity of the water body. In term of sustainability, this index could reflect on the water body responses due to nutrient additions from surrounding watershed.

It is hard to recommend "ideal" index/ There were rather multiple attempts to measure the "health" of aquatic ecosystem. As for me, I used eco-exergy, based on Sven Joergensen studies. To assess it you need to know biomasses of principal components (see attachments) Ecosystem health assessment is extremely interesting and fruitful topic!

Yours

Eugeme

I'd rather measure the basic limnetical variables and try to correlate them with a diversity index or a rarefaction analysis on an a assemblage you feel comfortable with. General indexes may be wrong due to every ecosystem is different in its community structure and in the way water chemestry and physics works. I suggest deepth, temperature, turbidity (not transparence that is what a Sechii disc measure), pH and phosphates. Some species are high sensible to these parameters and may tell you what is happening. The only problem is that you will need to know the richness or the diversity of species of similar waterbodies.

Article Fish community structure in freshwater karstic water bodies ...

As you are concerned about the physico-chemical parameters, you can focus on DO, COD, Chl contents, P, N etc. You can correlate the biological indices also with these variables as suggested by other researchers. 

Ideal is a dream reality, impossible possibility! Suitability of index depends on the parameters studies by a researcher. More holistic will always desirable so as to reflect the whole picture of an ecosystem as far as practicable. Some indices presents partial picture. The following are the indicators that integrate major environmental information in an ecosystem:Trophic index, WQI, Coeeficient of pollution, EHI, Eco-exergy Index, etc.

The physico-chemical parameters such as water temperature, pH, dissolved oxygen, oxygen saturation, conductivity, salinity, secchi disc depth, nitrate, nitrite, orto-phosphate, sulfate, chloride, total hardness, calcium and magnesium were analyzed in the water samples. Water testing can provide in-the-moment values and aid in determining the best course of action for a specific water body, whether a treatment is needed or an aeration system should be installed. The amount of dissolved oxygen helps to determine what species of fish, if any, can survive in the water.