First is the custodianship, it is of paramount importance to wallet which is self custodian. Secondly is security and this is mostly achieved by using a cold wallet but there I also own hot wallet to store some funds for easy access. The cold wallet are where the huge funds are saved in. Thirdly is choosing an open source wallet, there are self custodian wallets that are closed source and it is entirely frowned upon.

The transaction fees are also important but not just like the others listed above. The transaction fee problem is solved by using a wallet that supports the RBF opt-in. With this I could navigate around the amount of transactions fees to use.

The most important thing before choosing a wallet is the security of the wallet. Because if the wallet is not secured then our money will never be safe there. We should avoid using wallets that have weak security systems. That is, we should always avoid wallets that can be easily accessed by others. Because when our wallet security is completed then our resources will be safe in that wallet.

No matter which wallet you use, we must pay a transaction fee when making a token transaction in every wallet. The transaction fee from one wallet to another is not very high.  We never use wallets with less security due to small transaction fee variations. We should always use a strong and high security wallet even if the transaction fees are a bit high.

The community that it has got and the security that it offers. There's a thread in the Beginners and Help about this topic.

--> [General] Bitcoin Wallets - Which, what, why?

Aside from that, it's also best to stick with those wallets that have been known by most and has proven to be a reliable wallet. There have been newbies that are still being misled to the usage of web wallets that don't even provide them their private keys.

And that's one factor that everyone should take, upon using a wallet, use the ones that's providing them the private keys and they're the non custodial wallets.

You are right, cryptocurrency wallets are a lot. Also, there are many different types of wallets, which you forgot to clarify. When choosing a wallet of different types, you have to take into account certain features each time. In general, I would like to highlight the following thoughts.

If the most important function of a wallet is to save money, then security comes first in importance. Technical support is next. Without this, it is almost impossible to keep the security of the wallet at a high level due to rapidly changing trends in technology (attackers will simply hack a wallet that will not be updated). The next parameter is the simplicity and convenience of the wallet, which allows any user to master and use it.

If you're want to use wallet for your cellphone, the best choice is Electrum.

If you're want to use wallet for your PC or Laptop, the best choice is either Bitcoin Core or Electrum.

If you're want to hold for long time, you can use hardware wallets e.g. ledger or trezor.

You will not regret if you use this wallet because this is the only wallet which give many features and very safe. I don't see any reason for you to choose other wallet than I mentioned above except you know what you're doing.

1. Custodial vs Non-Custodial   2. Open source vs Closed source

These two points of mine are very important for everyone to understand before choosing a crypto wallet for storing their digital assets.

Custodial Wallets

are wallets that takes control from users and decide to be their users private keys keeper, meaning they function just like the banks, they keep your assets for you, with this, many things can go wrong, they can decide to close down the business, and they will leave with your money, they have the keys in the first place.

Non-Custodial wallets

These wallets are better than custodial wallets because they give users access to their private keys or recovery seed, even if they go down some day you can easily import your recovery seed into another available wallet, everyone prefers using Non-custodial wallets because they are safer compared to Custodial wallets.

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Open Source vs Closed Source

Open source wallets are more transparent, they leave every codes opened to the public, so when choosing a wallet, make sure they are open source, closed source wallets are secretive, they decide not to share their coding and stuff to the public experts and developers for full transparency, some said they are trying to avoid copycats and stuff, but users still prefer open source wallets and it's the best decision ever.

It is an obvious answer, the reputation of the site and developer that creates the wallet. At first, I use only the Bitcoin core wallet and I am skeptical to use other wallets, then I found Electrum, being light and easy to access without downloading the whole blockchain data, it is now my goto wallet.

Btw, I just browsed the Bitcoin.org wallet list database and it is surprising that they have a helper now.  They give options on the type or kind of wallet the downloader wants so the user can choose what type of wallet they prefer.  They even have choices like this

Self custody wallets are different from open source wallets, a wallet can be a self custody wallet but be closed source, for example coinbase wallet is a self custody wallet, but it is closed source and hence not recommended. The most recommended are wallets that are open source and self custody.
A desktop wallet isn't a hardware wallet, they are two different types of wallet. Electrum for example is a desktop wallet and also a mobile wallet, so you can run it on either a computer or a phone, but in a computer it comes with better features. A hardware wallet stores your keys offline in a small device you buy and keep physically.

I consider a wallet if it's a decentralized wallet and a non custodial wallet, any wallet i will have to use must be an open source cold storage, not all cold storage were open source, i try also to make use of wallet that are common and not only that, those that are reliable that can secure my asset for life, wallets like hot wallet are not reliable because they can be hacked or closed at anytime,when the source code of a wallet is made publicly available, they you can go for it as an open source, generate your keys and safe keep them to always use whenever you wanted to important your wallet on any device at anytime.