I have quite a bit of experience here that people may find helpful, and I'm going to share it in some detail; but since this comment is pretty long, let me give you the TL;DR first:

Water good, use plenty, daily. Soap not so much, use small targeted doses. Natural oils good, use after soap. Shampoo bad, but maybe necessary; minimize use. Other "skin care" products mostly harmful. Avoid.

Now for the details and my experience. First of all, I live in the humid tropics, on a farm with animals, so the environment is on the extreme side in terms of demands on physical hygiene. Secondly, this is Brazil, and Brazilians are if anything even more averse to any trace of "BO" than North Americans, and they are more likely to tell you if they think you stink, so there's that. And thirdly my wife has as sensitive a nose as anyone I've ever known, and she has an allergic reaction to a lot of strong odours.

I believe, and it is consistent with my experience, experimentation and research in this regard, that when healthy skin is clean, slightly oily, and protected by a healthy "microbiome", it almost never has a strong "BO" smell. What people call BO is actually mostly the smell of certain opportunistic bacteria overgrowing when there aren't others to keep them in check... the more you eliminate it with soap and "personal hygiene products", the more of it you have soon after the slightest bit of physical activity.

However, note that I said "clean" skin. If your skin is dirty, depending on the nature of that dirt it can serve as food for all sorts of other bacteria and/or have its own smell.

So how do you keep your skin clean while keeping its microbiome intact and healthY? With water. Just water, but plenty of it; we never shower less than once a day, and often several times. Preferably not chlorinated water... this may be a key factor that's often overlooked in this conversation, and may limit the extend to which other people can follow my personal regime with the same results... Chlorinated water may disrupt your skin's microbiome even without soap, I really don't know. We use water from our own well (it's all we have anyway). But if you do have pure water, you don't need much else for skin hygiene.

When I do use soap, normally only on my hands and privates, I always spread a bit of natural oil afterward. I use coconut oil; just a few drops on the hands which I then spread on my still wet skin wherever I used soap. This compensates for the oils the soap removed; think of of the process as an oil-change, remove dirty oil, replace with clean oil. The quantity is small enough that it is mostly absorbed by the skin right away, and the skin never feels oily, but rather silky smooth and cleaner than without the oil, and it stays that way throughout the day. This is particularly helpful on the privates... once you make this a regular practice, you'll never want to go without.

Soap is certainly a powerful and useful tool for cleanliness... we know that it is potent at disrupting bacterial biofilms and even destroys viruses, so soap is a good thing in its own right. After handling animals or sticking my hands in the soil I wash my hands with soap. But overusing soap on the whole body is very harmful. Using a lot of soap strips your skin of both the oils on the cell membranes that are part of every cell's normal functioning and barrier to the outside, as well as the functioning bacterial communities that exist in an equilibrium that normally prevents the overgrowth of any specific (smelly or harmful) bacteria. So if you use soap at all, use it only on those parts that are most exposed to "foreign" bacteria which don't belong on your skin, and always follow up by replacing the oils the soap strips off.

The soap I use is the simplest soap I can find, just soap. When I lived in the US I used Dr. Bronner's. Here in Brazil I use diluted liquid coconut soap. In general, I much prefer liquid soap, as I find it easier to use in targeted way and I find it rinses off easier.
Avoid any artificial scents and additives... they don't help anything and some of them may even be dangerous; none of this crap is regulated, and we really don't know much about what most of these chemicals do to organisms.

As for shampoo, it's a bit more difficult. Generally most people can get away with shampooing a lot less, and after an adjustment period the hair will get a lot less oily. But hair does accumulate crap that just water won't remove so easily and you will need some way to get it really clean now and then. Heavily diluted soap works in place of shampoo, but I for one use shampoo once every couple of weeks or so, and when I do I have to use conditioner as well or I won't be able to pass a brush through my hair afterwards. Some people just use diluted soap and follow with oil on the hair as well. YMMV.

I don't use any other "personal care products"... as far as I'm concerned that whole industry is 99% marketing; billions of dollars worth of crap that does more harm than good. When I travel to colder or drier climates, I bring my coconut oil and use a bit more of it on the whole body and that's all the moisturizer I need.

Now as for the people in this thread who seemed sceptical... I assure you, I'm at least as clean and probably smell better than you, and the people around me are not just "being polite".