first what level are people dressing and how often can you clean them/dry clean?
I don't know about that business casual definition above...most of what I see is dockers...some sort of button down shirt (short or long sleeve) and anything but sneakers.
Being it's an internship you can probably dress down a bit...if it's a place you are looking to work later it may pay to dress up.
When I worked in suits, I started with just two I got at JC Penney for $300 the pair I think. I added 3 extra pants to each. I picked up dress shirts, ties, and socks on sale...along with shoes.
Many I worked with re-wore pants and even shirts several times. I didn't.
I drycleaned weekly.
in business casual now I wear once and launder weekly.
Expect to replace each year or two.