For business casual I would start with a navy suit sans tie. It looks sharp but not too formal, and it's always better to be dressed a bit smarter than a bit more casual than everyone else in the office. Button down shirt is fine. If you arrive and everyone is in jeans and t-shirts, just leave the top 2 buttons undone, take off your jacket, and roll up your sleeves - you'll look a bit overdressed but not too much.
Then once you've assessed exactly how casual everyone else is, you can scale it down a bit. Dark/mid-blue or mid/light grey sport coats (or brown), maybe with some pattern (herringbone, subtle windowpane etc), with mid-grey flannels or tan/stone coloured chinos, or good jeans. Casual suits e.g. dark blue linen, tan solid, light grey flannel look great. For shoes try dark brown leather monk straps, chelsea boots, or mink suede oxfords; loafers in spring/summer. This is a chance to wear all that smart/casual stuff that formal business environments don't allow, and which can be a bit too smart for many social occasions nowadays.
A good smart/casual standby where a suit (even without tie) is too formal is mid/dark blue sport coat, light blue shirt, and tan chinos, with dark brown suede oxfords and a brown leather belt.