There are loads out there. The pattern from Wearing History [PDF] is nice
http://wearinghistory.clothing/e-pattern-circa-1917-combination-underwear-chemise/, and can be cut to any length. I like it because it has a nice wide neckline, that you can run a ribbon through to draw in to whatever size you need.
Cotton is just the fibre, cotton lawn, drill, poplin, twill sateen blah blah are the weaves. No such thing as 'bog standard cotton'
I have also one made in silk, which is short as I didn't have much fabric! A true 'cutty sark'
I have several chemises [and combinations, and drawers] mostly made from old, well-washed cotton sheets that are really soft. SOFT, no itchy scratchy left in as the bunching caused by the corset will kill you! You can get away with any old camisole though if you must. I don't recommend using stretch fabric as it may stretch in the wrong ways when stressed by the corset. Same for bias.