Summary: choose natural materials such as hemp, jute, organic cotton, or bamboo, preferably from a manufacturer that uses vegetable-based dyes, is fair-trade certified, and is working on reducing its environmental impact. Try to find shoes that last long and only buy new when you really have to.
The biggest environmental impact of shoes comes from the used materials and the manufacturing process. If you also value 'social sustainability' you should also factor in the working conditions of the people who create the shoes.
According to Nike materials make up around 60% of the environmental impact of its shoes. Especially leather, synthetic plastics, and certain hybrid materials have a big impact, but also cotton, dyes and glues.
The big impact of leather comes from raising cattle and the chemicals typically used in the tanning process (chromium). Plastics and hybrid materials are usually made from oil, and cotton is grown using lots of water, fertilizer and pesticides. Dyes and glues contain chemicals that negatively affect the environment as well as the health of the workers that manufacture shoes.
Vegan leather isn't necessarily a more sustainable choice because it can be made from PVC which is one of the worst types of plastic.
A typical pair of synthetic trainers generates 30lbs (13.6 kg) of emissions, equivalent to leaving a 100-watt bulb burning for a week (source)
Most shoes are made in Asia, but surprisingly transportation is only a small part of a shoe's carbon footprint. Researchers from MIT did a life-cycle analysis of an ASICS synthetic sport shoe and found that transport on average only accounts for 3% of the shoe's carbon footprint, and at most adds up to 7% when shipping to Canada (about the farthest country from China where the shoe was made). Raw material extraction and processing accounted for about 29% of the total carbon footprint and the manufacturing process was responsible for 68%. The reason why manufacturing has such a large footprint is because a single shoe consists of many parts that require multiple processing steps for assembly. The machines in Asian factories that perform these steps typically run on electricity generated by coal.
Developing countries like India and Bangladesh, and to a lesser extent also China, do not have strong worker safety or environmental protection standards. Sweatshops are common in these countries and there have been many reports about child labor. Workers are often exposed to toxic chemicals and left-over chemicals are often spilled or dumped.
There are a few blogs that list fair-trade and sustainable shoe manufacturers (e.g. this one and this one) but the downside is that it's difficult to compare between listed companies. Alternatively you could do some investigations yourself. You already mentioned Rankabrand in your question which can be very helpful. A similar website is EthicalConsumer.org which has a section on shoes with interesting background information, but the newest company reviews there are behind a paywall.
If a shoe manufacturer is not listed anywhere you can use the Internet to find out more. Especially look for information if the manufacturer is:
- using or switching to environmentally friendly materials,
- using or switching to renewable energy in their factories,
- trying to reduce the number of processing steps in manufacturing.
- was involved in child labor or dumping scandals in the recent past.
Good materials to look for are natural materials such as hemp, jute, organic cotton, bamboo, vegetable-based dyes and to a lesser extent recycled plastics. If you are really set on leather, go for vegetable-tanned leather or better yet Piñatex.
Unfortunately it's hard to tell in advance what the quality is of a pair of shoes and how long they will last, otherwise you could take that into the equation as well. The least impact comes from not buying new shoes often and wearing your old ones as long as possible.