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For someone who values anonymity & privacy, what is the recommended way to pay on the Internet?

Example: To buy a domain or a VPN or another service

I know that we can use cryptocurrencies, but at some point, you need to buy cryptocurrency using a traditional currency.

To protect your privacy and avoid tracking, nothing beats cash.

There are various services that let you purchase credits in cash at a brick and mortar store, which you can then later use to purchase goods and services online.

One example is paysafecard (I haven't tried it, but you should also be able to buy bitcoin with cash). There are a number of VPN providers which accept these payments.

Alternatively, you could simply purchase your VPN access directly offline at a store.

There are also domain registrars which accept these payment methods, but most will ask for identifying information (name, address, etc) when registering a domain. So if you want to conform with registrars TOS, registering a domain anonymously would not be not possible. You can hide your information from third parties by requesting that your registrar doesn't disclose the information, violate the TOS by providing false information (not recommended), or find a registrar or third party service that does not request this information.

VPN wont make you anonymous.

The owner of the VPN service will still knows who you are (origin IP address).

In the past several VPN providers that stated everything was anonymous released all information they had to the FBI and USA department of justice.

Makes sense that they are not private, if you commit a crime using their systems if they cannot point it to you then they will be liable.

For the crypto currencies you do not need to buy them you can mine them.
Also there is some with higher level of privacy than others.

At the moment the best possible way to make you private in some of the internet traffic is still TOR as long you follow their best practice.

The other way to be private in the internet is if you steal someone else digital identity. This is the most common means used by thieves.

You can trade cryptocurrencies with other cryptocurrencies and the trails become cold fast if you use random amounts. More iterations with independent wallets makes it even harder to trace. Of course you lose some money in the process and it takes some time and effort. That's the price for such anonymity.

Sadly the same methods that are used for money laundering applies to making payments truly anonymous.

You could use xmr.to for that.
According to them:

XMR.TO allows you to make a Bitcoin payment with the strong privacy provided by Monero. This means that using Monero together with XMR.TO, you can pay any Bitcoin address in the world while protecting your privacy.

You buy Monero, a privacy-centric coin, send to xmr.to with the destination Bitcoin address, they sell your Monero, buy Bitcoin, and send to the host. Xmr.to a well known service, and lots of people uses it every day.

Their FAQ is pretty informative, and you should read it.

You could buy gift cards with cash then sell them for bitcoin on r/GiftCardExchange

nothing beats bitcoin. so far, it's the meta anonymous coin to be used on the internet.
you can probably use it to possibly buy a disposable credit card from "semi-credited" sources (hypothetically, of course) and get vpn yeah? but it's not a good idea. VPN companies aren't mostly trusted imo, and those that are have a shitty product.

you want anonymity online? do what everyone does - TOR and bitcoin. simple enough.