hardware wallet
A Hardware Wallet is a device you have to buy. These devices are considered to be the safest wallet if ethers are to be used actively. Even malware on your PC cannot harm your Ether. Initially, the Hardware Wallet creates a seed of 12 to 24 words, which then creates your receiving addresses. In addition, the Hardware Wallet can store multiple digital currencies and not just Ethereum.

Advantages:

Safe storage of the ethers
Active use of the ethers possible
Other digital currencies (ERC20) can be stored
Disadvantages:

acquisition cost

The best Ethereum Hardware Wallets:

Hardware Wallet User-friendly Open Source Currencies
Trezor* Yes Yes Bitcoin, Ether and ERC20 Token, Litecoin etc.*
Ledger Nano S* Yes No Bitcoin, Ether and ERC20 Token, Litecoin, Ripple etc.
Ledger Blue* Yes No Bitcoin, Ether and ERC20 Token, Litecoin, Ripple etc.

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A Desktop Wallet is an Ether Wallet for the computer that you can download. On the ethereum.org website you will find several options for a desktop wallet, depending on your operating system. With a desktop wallet, the environment is very important, i.e. whether your computer Bitcoin Profit a free Software┬áis free of malware. Ensure a secure environment and keep your computer free of malware – at least install a permanently good antivirus program*.

Advantages:

Active use of the ethers possible

Disadvantages:

Vulnerable environment
Developer-dependent (updates, security, etc.)

smartphone wallet
You can also download an Ethereum Wallet for your smartphone, depending on your operating system. For all operating systems the Jaxx Wallet. It also applies to the Smartphone Wallet that you must keep your Smartphone free of malware, possibly with an antivirus program*.

Advantages:

No costs for creation and use

Ether can be taken anywhere
Disadvantages:

Vulnerable environment
Developer-dependent (updates, security, etc.)

online wallet
An Ether Online Wallet is a wallet that you create online at a website or service. The website creates the private keys for you and usually holds your private keys for you. For this reason, you should only use Online Wallets in emergencies or for small quantities.

Because as you learned earlier: You do not own your Ether until you have the private keys and keep them safe. Or would you buy a car and leave the keys and papers at the dealership?

Advantages:

Quick and easy creation
Useable anywhere in the world with email and password
Disadvantages:

Vulnerable environment (including phishing)
Holds your private keys
Depends on the service of the provider