I only find walls of texts about this topic, but no general things as how people would dress every day.
I remember vaguely that women are to wear skirts or dresses, gloves, and to cover their head.
I understand it might differ a lot depending on social class and work. But are there any pointers such as "men wore X type of shirt and hats were common"?
I think you have a misunderstanding of something here - a dress code is a set of standards laid out for how people in a particular group are required to dress, which does not apply to an entire population. People working in a certain office in 1885, for instance, might be required to follow a dress code that dictated colors they must avoid, proscribed types of jewelry, etc. but the average person waking up in the morning in 1885 was not following a dress code when they put on their clothing.
There are a lot of answers in the Nineteenth Century section of my flair profile that relate to how people dressed in the period. I hope that this helps you with your inquiry.