On YouTube you'll see a lot of How To videos that tell you to empty your bank account to buy a million things to start wet shaving. They imply that should you neglect even one of these purchases your entire shave will be ruined.

Necessities:
-Straight Razor
-Shaving cream or soap
-Strop
-Whetstone
-Shaving Brush*
The razor, strop, and whetstone do seem like a lot, but you need all three if you plan to keep your razor for a long time. You don't want to cheap out too much on these because remember, they are an investment. Buy one once and use it for 50 years rather than have it break or wear out and buy a new one in two years.

A decent Dovo blade will cost around $80. Avoid Art of Shaving stores, as they are ridiculously overpriced. You're honestly better off using Amazon or the vendors on this site. A strop will cost about $20-30, and a whetstone can cost upwards of $50 or more. Soaps and creams are much cheaper. I'd recommend using a soap over a cream, as they cost less and last longer. Edge Shave Gel and Barbasol are not great, but they fall under the category of "good enough" if you're looking for a low maintenance shave.

*Shaving brushes are not technically a necessity (unless you're using a soap instead of a cream) but I highly recommend getting one. It helps a little bit of product go a long way. You can use a dime-sized amount of cream with a brush and get enough lather for 2-3 passes, easily. It's also part of the classic shaving experience. But if you're using a cream, you technically don't need a brush.

Luxuries:
-Aftershave lotion/pre-shave oil.
-Alum block/styptic pen
-Hot water

These oils are nice and may make your skin and shave smoother, but they're not really necessary for a good shave. To be honest they're expensive and in my experience don't work that well. Some people swear by them but whatever.

You may nick yourself a few times, but I doubt you will need a styptic. The worst bleeders will stop after a minute or two.

A lot of shavers also swear by hot water, but for many (including myself) it only irritates the skin, especially if the blade is dull. You're perfectly fine shaving with lukewarm or cold tap water.

Useless buys
-Shaving mug
-Razor stand
-Brush hanger

Why use a shaving mug to hold your soap or mix your lather when you already have a perfectly good coffee cup in your kitchen? Shaving mugs are a waste of money. Anyone who buys one has too much cash to burn.

Razor stands are also useless. Straight razors fold into their own handles and can be stored that way. Even safety razors can be laid on their sides and be just fine.

While you should hang your brushes to dry them out, don't waste money on a brush stand. Take a paper clip or wire coat hanger, depending on the size of the brush, and twist it around the handle of your brush. Then hang it on a hook on the wall. You've saved yourself $45.

I hope this helps you spend wisely and save money. Above all, don't listen to the hyperbole about wet shaving where "you must do X, Y, and Z exactly or you'll have a terrible shave!" Don't listen to the "it took me a year just to be able to shave my cheeks with a straight razor" nonsense. With some practice you'll be shaving your whole face without cuts in a week. And speaking of cuts, I never got anything that hurt worse than a bad papercut. Doesn't mean you shouldn't be careful though.