WetShaving

It sounds like you might be talking about disposable cartridge razors or all-in-one disposable razors, like the BIC Sensitive razors.

We'll recommend that instead, you buy a double-edge razor, which uses small replaceable double-edge blades that you change out every seven to thirty shaves.

This wiki talks about double edge safety razors in the "Removable Blade Razors" section. https://en.wikipedia.org/wiki/Razor

I just transferred from Reddit, here’s my usual copy pasta advice for those who would consider a safety razor:

Look at these videos for a reliable introduction and guidance on technique for making lather and shaving.

I recommend one of the starter kits from either Maggard Razors or Stirling (the “basic” kit from Maggard or the “budget” kit from Stirling have all one really needs).

The standard Maggard razor head is modelled after the Merkur and the improved Mühle/Edwin Jagger heads, but you can choose a milder or a more aggressive head and they are so cheap that buying different ones is affordable. They offer an open comb head as well.

You’ll get a choice of steel handles as well. Maggard is in the US, but they have affordable shipping rates and tend to be cheap even internationally.

Brush and shaving soap are at least as important as the razor itself, traditional wetshaving is based on slick, wet lather that hydrates (and thus weakens) the stubble. Washing your face right before shaving helps as well. I step out of the shower and shave right away, still dripping wet.

As for the brush, synthetics are the usual starter recommendation these days, as badgers aren’t really good below a higher price threshold and boar brushes need a break in period to get soft and make good lather. A boar brush should also be “soaked” a few minutes before use, which means to wet the bristles with hand-warm water and rest it on its base. Immersing it is unnecessary and potentially harmful for the handle. Otherwise, the type of brush is a matter of taste.

What soap to chose depends much on your taste in fragrances and of course the quality of the soap base. For a start, all the soaps in the recommended kits are good. After that the world’s your oyster.

I’m in Europe and rather fond of traditional British, French, German and Italian soaps. Sadly not all brands offer the same quality as a decade ago and most British soaps are a shadow of their former self. I find DR Harris still excellent. A few quick recommendations at different price points are Pre de Provence and Martin de Candre, Klar and Speick, Cella and Saponifico Varesino. In the US, you have an abundance of newer artisans (Stirling, Noble Otter, Barrister & Mann, etc.) that make very good soaps in a wide variety of scents.

All double edge razor blades will fit all double edge razors aka safety razors. There are other kinds of traditional razors, like GEM and injector types that take single edge blades, but these are exceptions.

Razor blades are a highly individual matter and recommendations are less than useless. Test for yourself and trust your experience. (For me, the notorious Feathers are not “sharp” at all, they just tug and scratch, but they are amongst the most hyped brands on forums.)

So don’t bother about blade reviews or measurements, they won’t predict your experience, which is all that counts. Get a bigger blade sampler pack later (a good supplier for a vast range of brands is www.razorbladesclub.com) and read about how to use it.

A styptic pencil is handy for quickly sealing any nicks, so you don’t have to leave the house with patches of toilet paper on your face. I can’t remember when I last used one, but I still keep it around.

Some items are more or less optional (or superfluous, depending on your preferences):

A lathering bowl is for those who don’t like face lathering as shown in the video. I never use one, but some swear by it.

Razor/brush stands are not necessary (brushes dry equally well when standing up, once most of the water is shaken out), some people just prefer the looks.

Any aftershave treatment is down to individual preference as well. I only use a balm in winter, and nothing in warmer weather.

Traditional aftershaves are alcohol based and may be used for their bracing effect and fragrance. The necessity of any disinfecting effect alcohol may have is way overrated (if anything, one would have to disinfect skin before shaving!), but so are probably concerns about skin damage (except a drying effect on dry skin). Personally I always preferred to be able to chose to go scentless or use real fragrances, so I used alum for some decades - until I found that I didn’t need it anymore.

Alum and witch hazel are astringents and can help to seal microscopic cuts, thus soothing possible post shave irritation. Alum has even some styptic effect. On the other hand, it can be drying and even cause irritation for some, so the common advice is to rinse it off after a few minutes (like after rinsing razor and brush and cleaning the sink). Alum is often said to be an antiseptic as well, but that claim isn’t based on any medical evidence (quite to the contrary). It does have some antibacterial effect, just good enough to suppress bacterial growth on skin for a while, therefore it is also used as a scentless deodorant.