Big stuff, you'll be improvising with the shirt off your back, kitchen or blue paper roll, pallet wrap whatever.
I should buy a Israeli tourniquet / field dressing just in case. Those seem to be good. I carried an army style field dressing when I used to shoot and thankfully never needed it. Just remember to replace them once in a while.
For the small stuff, workshop isopropyl alcohol is a perfectly good antiseptic / degreaser. It hurts like hell so you won't want to put it on a cut to for sterilising and for cleaning around to help a dressing stick it works well.
Superglue doubles up for medical use
Betadine is the good cheap antiseptic.
Micropore for everything.
My new favorite : 3M Tegaderm dressings are less than a £1 each from the chemist. I sliced a matchstick wide strip of skin off my knuckle when a glass coffee pot broke in the washing up a fortnight ago and these have kept the wound clean and mobile while it's healed. They are like sterile, sticky pallet wrap but more elastic. The wound stays wet while it heals and it's gruesomely fascinating to watch how your body fixes itself