I don't want them to delay my case any longer and I guess it's better to send more evidence than less.
Ditto! It looks like although they do not directly mention this in the instructions, all the evidence of your legal entry and current status is what they want to initially receive with the application. New filers, make sure you always include the copies of passport bio page, visa page, current I-94, current and previous I-20s, EADs and such, everything that is related to immigration.