I just got the base game and the DLC of Drox Operative. Now I wonder if I should install the DLC right away or if I should play the bare base game first to learn the game mechanics and get used to them?

Will the DLC increase the difficulty or is it just additional content that will add more variety, but leave the difficulty untouched?

I would recommend to play with DLC straight away.
DLC adds high-level content without changes to mechanic.
You can miss low-level content if you install it after getting high level too.