I think private key wallet means you are importing private key. All wallets have a private key. Just create a regular new wallet and export the private key once created.
Mmm in that case it would work in a weird way: I selected "sign up" since I don't already have a wallet (there's log in as well) and it gives me 3 different wallets options: simple, brain and private key, and in order to create the private key wallet I need to complete the form before, including the private key field, which is blank
Use simple wallet if you don not have a wallet already.
This will create a wallet file on your computer with a new private key that will be secure by the password that you enter.
Do not enter passwords like "123" or "qwery" this is not safe because if someone gains access to your computer could
steal your wallet file and then brute force the password.
Once you have created the wallet you will be able to access the wallet by selecting the wallet from the list of wallets.
In case you purge your browser then you will have to import that wallet file with import wallet option and
then select from the list and use "sign in" and enter your password.
Do not forget your password or you wont be able to access your wallet neither your funds.
When you create the wallet make a backup of the wallet file and also of the private key.
The option brain wallet is to create wallets by using one single passphrase.
I would not suggest you to use that method i consider this insecure because a lot of people do not use strong passphrases.
So if you use somthing simple like "123" for your passphrasse remember that you will be hacked
becacuse "123" is everything that you or anybody else needs to access your wallet.
If you really want to your a passphrase i suggest you use at least 50 + more characters letters upper lowercase and special character passphrase.
The private key option is used when you already have a NEM wallet private key.
that could be the private key from your NCC or Android or IOS wallet that you can export from there.
I hope you manage.
If not we are here to help you.