For "basic sewing supplies" I take to classes I use a bag that Bernina used to sell. It looks and works sort of like a large cosmetics bag (sort of like a notebook) with 3 "pages" of zippered compartments and large compartments on the inside of the front and back. In it I have:
Machine needles
Hand needles
A flat pincushion with a loop that I hang on my shirt button
Extra Pins
Three pairs of scissors (dressmaker shears, a small pair with sharp points; scissors I can cut paper with)
Rotary cutter
Stiletto
3 spool of piecing thread (white, black, tan)
a list of feet I already have for my machine (so I don't buy it again)
square ruler
ruler for straight cutting
Permanent marker
Pencil and Pen
Small pad of paper
Post-it notes
point turner (you could use the stiletto if it's not too sharp)
I never unpack it and try not to borrow from it - the items were bought just to take to classes.
I put that in a cloth recycle bag and add as needed:
small cutting mat
longer ruler
small iron
Extension cord
specialty threads
fabric
pattern
I take my machine in its travel bag if I have to take a machine - and make sure I take a "table" that fits around the machine to have a smooth surface to sew on.