If you already have another wallet on another computer you can just transfer your wallet.
This would be very un-secure if the other computer was not yours. The online wallet is the most convenient way to store your BTC and altcoins. Different online wallets have different security measures and available support. It is highly suggested to use an established online wallet and a reputable one.
Other online wallet providers do offer access to the private keys this is different to your password but again the reputation must be considered when choosing. At an early stage in crypto, this is irrelevant. You can access your online wallet from any computer connected to the Internet.
As with any online service, there is always a chance of hacking or misappropriation from inside the company and your funds could be lost.
If using a computer that is not yours, this increases more insecurity as someone could have installed spyware and then they will have your password and can steal your BTC. Some wallets can also store multiple coins including BTC.
You just need to research the wallet before selecting. Always consider security, the support, and the reputation of the exchange a priority when making a choice. Use an Exchange for what it is intended, buying and selling BTC and Altcoins, not for storing them longer than necessary.
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A backup USB provided which should be kept secure.