What is the lowest enough speed for mining?
Internet connection speed will not impact your mining process. This is depending on the number of machines you are using for mining or the number of clients hashing. Look up the stratum (open source client-server) protocol, and you can find out about how much bandwidth each client will consume for the process.
I actually have this same question before because I understand that there are mining farms in remote places of China where internet connection may not be at par in urban areas. So this is not really the critical one as long as there is an available internet connection. Thanks for clarifying this question.