What the best recycling policy is is a political question. As you mentioned in your question there are many aspects to this and all good recycling policies will address issues such as cost, environmental impact, human health impact, end-user awareness, convenience of using the system, compliance, amount of generated waste, worker safety and more. Which aspect is considered to be most important is often reflected in national or local waste processing laws. Besides politics, local circumstances such as market prices of recycled materials and the availability of processing facilities and landfill areas can have a big influence.
I'm not very familiar with recycling policies outside of Europe, but many European countries put emphasis on achieving high recycling rates.
If you look at this blog post for example you can see that several European countries (and South Korea) score high on municipal recycling rates. Part of the reason why European countries score this high has to do with the various EU directives on waste processing and environmental protection. EU directive 2004/12/EC for example says that:
Recovery and recycling of packaging waste should be further increased to reduce its environmental impact.
Implementation of this directive is however left up to each EU member state and consequently there are big differences between EU countries. Countries like Germany, Slovenia and Austria score 55%+, where as others such as Slovak Republic, Greece and Portugal score 11 - 26%
Source: page 50 of the OECD document 'Environment at a Glance 2015
To achieve high recycling rates, multiple waste streams are a necessity, because mixing different waste streams causes contamination of the materials and reduces their recyclability. However, keep in mind that recycling rates can be misleading. They are difficult to compare because of the different definitions of (municipal) waste and the different methods of calculation. Also municipal waste (which I assume your question is primarily about), is only a small fraction of all generated waste. Roughly about 10% of all waste is municipal waste, but it does account for about 1/3 of the costs.
In terms of waste policy EU directive 2008/98/EC is interesting which says:
The first objective of any waste policy should be to minimise the negative effects of the generation and management of waste on human health and the environment. Waste policy should also aim at reducing the use of resources, and favour the practical application of the waste hierarchy.
The waste hierarchy describes the methods to process waste from most favourable (e.g. reuse) to least favourable (e.g. dumping in landfills). What you often see is that countries over time slowly work their way up the hierarchy and start using more 'advanced' waste processing methods. For example, the EU recently proposed to ban single-use plastics, which is a measure that belongs at the top of the waste hierarchy (prevention and minimization).
As an implementation example, let's look at The Netherlands (because I live there and because it does fairly well). The Netherlands has a recycling rate of 51%. In Europe only Austria, Germany and Belgium are doing better in terms of recycling rates (based on page 13 in this document)
All cities here separately collect wastes types such as paper and cardboard, kitchen and garden wastes, glass, PET bottles, clothing, and batteries. Some cities also have a separate stream for what they call PMD which stands for Plastics, Metals and Drink cartons (e.g. Tetrapak) and claim that separating these waste types by end users is the most effective method of recycling. Other cities disagree with this and claim that separating these 3 waste types from a 'general other' waste stream is more effective. So far I haven't seen a final conclusion in this debate.
This week the Secretary of State who is responsible for waste management announced that The Netherlands has to transform into a full circular economy (news article in Dutch). This goal should be achieved by 2050. One of the major steps towards this is to make improvements in product design; all products should become repairable, reusable and/or recyclable by design, and may not contain any harmful substances.