Do I load all files at once or one at a time?
Since the process can be run independently on every file/batch, I would tend to recommend processing each file one by one for the sake of scalability:

Depending on the details of the task there could be some minor optimizations which can be done only by processing the whole data at once, like things related to I/O and memory usage. I can't think of any significant improvement obtainable this way.
By itself processing the files independently won't bring any performance improvement either, but it has a massive advantage in terms of scalability: the process can be distributed easily by using multiple cores and processing any number of files on each core. This option offers flexibility for processing the current data (if you can afford multiple cores/machines, the process can be faster) and importantly any future version of the data, even if it grows very large.