Dirty = Infected = Dead

Reading, in my spare time, Florence Nightengale's Notes On Hospitals, what becomes rapidly apparent, in a tome from when Pasteur's germ theory was still largely theory, was that even then, anyone (like Florence) who spent 5 seconds looking at the problem noticed that building medical facilities that were third-world dirty and rampant with lice, flies, rats, shit, etc. was a passport to 50% mortality levels. Which she published, to rave reviews, after having reformed British Army hospitals and cutting casualties  to less than 10%, which is pretty amazing given the primitive level of even the most advanced mid-19th century medical treatment, let alone for field hospitals in a wartime army.
 
Clara Barton did the same thing over here a few years later during the Civil War, with similar results. (It's also significant that neither the British nor American military supervision had either the wit nor wisdom to figure this out their ownselves, despite having actual degreed and medical-school trained professional doctors to figure it out. Nightengale was a nurse when the only requirement to become one was to put on an apron and do it - no schools, no diplomas, no nothing. Medical education from 20-30 years prior was obviously nothing to write home about, and the bureaucratic mentality - or rather, its lack of any - has been unchanged for six millennia, since before Pharoah's time and back to Hammurabi, probably.)

So, besides the historical note, so what?

In anything from a nasty regional disaster, to major societal upheaval, you're going to be in similar circumstances in a hurry. And the lesson at the individual level is exactly the same:
You can't provide care for anyone that's worthy of the name, if you're working up to your elbows in filth.

So, some notes for you, at any level.
1. Wash your hands. Always. Frequently. Compulsively.
2. Expose and clean the patient.
3. Clean everything, on, over, under, and around the patient, with religious fervor.
4. Before and after EVERY patient.
5. Then do it all again.
6. Literally, lather, rinse, repeat.

Now, some details.

Soap and water are your friend. And warm to hot water are way more fun to wash in than cold water. You lather and wash for the same length of time the "Happy Birthday Song" takes, then rinse, getting all the nooks and crannies around fingernails, and you're as clean as you need to be for 95% of medical work. (Surgery standard requires repeating with povidone iodine scrub and finger brushes, then rinsing that too, before gloving in sterile gloves, gown, cap, and mask. Just saying. Surgical Scrub 101 for med students YouTube video)

Alcohol is for sterilizing instruments, not wounds. Write that on your hands in indelible ink, and don't wash it off. Alcohol, given 15 minutes to work, will kill the cooties on most everything. Provided you've first scrubbed the thicker accumulations of yuck off of them.
It's also inflammable, kills healthy tissue, and burns like hellfire in open wounds. If you use it on your patient, EVER, you deserve to have them cock-punch you. And if you set them on fire, even accidentally, nobody will cut you any slack. Save the isopropyl alcohol for instrument baths, in a covered basin. Period. And remember the "inflammable" part.
Bearing this in mind, where wash water is scarce or unavailable, alcohol hand sanitizer gel is better than not washing up at all.

Hydrogen peroxide is for getting blood out of clothing, carpets, etc. Not for sterilizing anything. It works poorly for that. Need to get bloodstains out of your scrubs? Great stuff. Need to get bloodstains out of the carpeting before the cops arrive, after you hide the body? It'll do that. Sterilize a wound? No way in hell. It also burns like hell, it foams up and makes you think it's doing something, but it's really only cleaning superficially, so it hurts plus it misses things. Two bad things for one low price. Save it for getting bottle-blonde, or cleaning blood spots out of linen or clothes. Not for patient care. If you want to use it for very minor wound cleaning, to assist in getting organic (bodily fluids, etc.) stuff up and out, and decrease germs (NOT eliminate them), it's not terrible for cleaning up an infected toenail, or making sure you cleaned everything off a pair of tweezers. But it's never the last, let alone only, agent to use. With other things, okay. Alone, never.

Betadine (c) (trade name) or povidone iodine (generic name) is the standard - if the patient is not allergic to iodine. Iodine allergy, or shellfish or seafood allergy? No iodine, period.
Use solution (the weaker formulation) not scrub (the stronger one). You can and should even cut it 1:1 with either clean tap water, or any form of sterile water or sterile saline, and it makes an excellent wound soak. You can pour it or blast it (with an irrigation syringe) straight into open wounds, to kill the germs you're dealing with in a dirty/infected cut. Just suction it mostly all back out after a bit, once it's done its job.

After that, there are a host of engineered antiseptic chemicals. the most commonly available commercial one is benzylkonium chloride (abbr.: BZK). It's in all sorts of handiwipes and such. It is the lion's share of what makes Bactine (c) work. It hurts far less than alcohol or hydrogen peroxide, and cleans one hell of a lot better, along with having no allergy issues for people with iodine problems. Therefore anything with this should be your first-line choice. Povidone iodine should be used afterwards, if there are no allergy issues. And lastly, clean water and soap. Phisohex etc. is okay, but so is Ivory.

Next is simple household bleach. You can look up all sorts of dilutions for it's use, bearing in mind it is for things, not people, and it, you know, bleaches things. Like your clothes, when you splash it. At four to eight drops per quart, and given 30 minutes or so, it'll turn a canteen or jug of water into clean water. At higher concentrations, you can make a slurry that'll kill anything, including biological and chemical agents. Which is handy when you're having to decontaminate an impermeable surface on a treatment bed or what have you that got someone's blood or diarrhea, etc., on it. You should have handbooks or cheat sheet cards made and laminated that tell how to do all of the above. And get an eyedropper too.

Hint: Put the eyedropper inside a 4"-6" section of end-threaded PVC sprinkler/plumbing pipe, and screw on pipe caps at both ends. Drill a small hole thorough one cap, knot a piece of cord inside, and tie or loop the other end through your laminated instruction card, and over the neck or handle of your bleach bottle, and you'll have a crushproof container for the dropper to make your bleach solution when you need it. If you need a small plastic measuring cup for stronger mixes, add that as well.

Lastly, if you want to go with potassium permanganate, it can, just like household bleach, be used to purify water, make a cleansing wound wash, etc. (If you look up the details, it can even make an improvised incendiary device. NTTAWWT.) So be careful lest you set your own stuff on fire accidentally, if you choose to stock it.

There are literally catalogs full of other items and solutions you can use and should acquire, some for cleaning surfaces that aren't people, and others for use directly on people. Anything else you get should be studied exhaustively. You're responsible for everything you put on, in, or next to people you treat. Get the MSDS sheets for all of the above, because the stuff you use to clean will splash someone in the eyes or mouth, and you'll want to know what to do if that happens too. And for pete's sake, store your stockpile intelligently, so it doesn't corrode your cabinet, mix with other chemicals and make a toxic brew, or burn your stuff down. All chemicals should be treated with the same diligent care you'd use for unstable nitroglycerin or a running chain saw, and you'll never need to treat yourself for screwing things up. Murphy is a bitch.

And stockpile as much of any of the above as you can justify. Pool shock can make gallons of liquid bleach. Bar soap lasts for decades without going bad; so does liquid soap in jugs.
Alcohol is a flammable, as noted. Hydrogen peroxide will, over time, turn to tap water (H2O2 becomes H2O), even in brown light-resistant jugs (yet another reason why it's a poor choice for long-term stocking and usage). And so on.

Bear in mind you'll need sponges, mops, wipes, and other cleaning supplies, and the more people you contemplate treating, the more cleaning stuff you'll need, in small mountains. The only way to make something clean, is to make something else dirty (i.e. clean floor requires a dirty mop and bucket), and that goes double for trying to create any sort of clean or sterile area for minor, let alone major, surgical undertakings.

On an individual level, hand sanitizer gel, betadine, and BZK wipes and solution should be in every kit you stock, without fail, down to the smallest one. Leakproof travel bottles for TSA use are perfect for keeping a small quantity of each in a personal/car/field kit.

You would also be well advised, living in nice, clean, lemon-scented first world conditions, to make sure you can deal with rats, mice, body lice, bedbugs, fungal infections, and a host of other nasties that will crop up when everyone reverts back to a weekly bath/shower, when they're lucky. The plague spread very nicely in medieval through industrial times, when everyone had their own supply of body and hair lice 24/7/forever.

So do you want to guarantee 50% casualties, or less than 10%?

This concludes your hospital cleanliness briefing. Screw it up, and kill your patients, and/or infect or infest yourselves.
Don't be that guy.