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.
What you said is correct but the main point is that what ever internet connection to be used but it should be stable one because if the connection is not stable then the the reward block cannot process fully and it will be cancelled so like this you wont be able to earn any thing. So stable connection is the more important in the mining process. Like what other user told 128 kbps is also enough to run the mining until the connection is more stable.