I have to shave my face and skull every day. My beard hair in particular is dense and metallic (imagine every fourth beard hair looks and feels like a short sharp brass wire) and extremely hard - so my blades often chip and can become unusable after a single shave. For irritation and cuts, against or with the grain makes zero difference, but does for detail patches. As you can imagine, this gets expensive, so I've been experimenting with razors for a decade. Here's what I've discovered for me - YMMV.
1. Electric Razors, including the most expensive well reviewed one on the market, don't actually do anything - literally. I can pass the shaver over short, medium or long growth and it simply doesn't do anything, not even catch for the most part. It's literally as if I left the plastic cap on the damn things. Apparently that's just a thing. Some people can't use electric razors.
2. The cheapest least advanced razors to do a halfway decent job are Schick Slim Twins. If they're on sale, it's a good budget alternative. Definitely only able to shave once with these though, and their lubricant, whatever it is, is fine. No irritation and smooth shave, but takes about twice as long as the best one.
3. I have entirely by feel - with and against the grain. The hardest parts are at the base of my neck and I have to shave these against the grain multiple times before the razor angle catches the base of the hair. Although only the second most likely for me to miss and realize too late.
4. Discovering a missed patch on the road is the WORST. Smoothing my scalp or face and discovering an isolated copse of unshaved vagrancy is awful, so I ALWAYS travel with spare razors in my car and backpack to address on the fly. Such a relief. Scares other drivers though watching a skinhead dry shave in the car (or occasionally a surreptitious concealed movement on the plane).
5. I can shave using a fresh razor without soap, water or shave gel - completely dry - and have done so dozens of times in emergencies, or camping or in the snow where I don't want to wash in a glacier fueled cataract. I ain't Ryu.
7. My favorite disposables of all time are Bic Flex 5 and their weird "budget unisex" Bic YOU - which are way cheaper than Flex 5 yet almost identical design and blades - the difference is that the holder doesn't pivot or rotate on a ball, so you're in charge of angling the blades - which is fine for my style.
8. Replaceable safety razors are worse than most disposables.
9. Cut throat razor is an absolutely ABSURD amount of effort for a face and skull every day and is reserved solely for a spa treatment type experience and further, keeping a razor sharp yourself is a fool's errand, and even high quality steel will chip on my hair (Barber is furious) and some of those can't be whetstoned out and have to be ground. IT is possible to do it yourself safely, but the traditional folding handle is designed to be used on the face and further, by a third person, so cuts or mistakes are INEVITABLE.
10. I seldom wear aftershave or a balm, but occasionally if I'm forced to use the same blade twice, I will apply a tiny dot of sandalwood and aloe to reduce potential redness.
11. I used to use Dollar Shave Club, but they switched manufacturers, I suspect, because the before and after difference was ABSURD. Although they had good customer service.