
-Blockchain.info
-Xapo
Pros
-Easy to use
Cons
-No control over funds
-Can't access some features which having the private key can do
HardWare Wallets
These are HardWare wallets are some of the strongest wallets that you can have, you usually own one when you have a massive amount of bitcoins(btc) you don't want to store on your device. With those heavy duty wallets its near impenetrable and extremely resistant. Here are some examples of them
-Trezor

-Keepkey

-Ledger

Pros
Incredibly secured
Long lasting
Offline/Cold
Cons
Expensive
Desktop Wallets Now we are getting in to the wallets you should use personally if you just want to store a couple bitcoins.
These are the wallets that can be used everyday and are quite safe if you know around them.
-Electrum
-Bitcoin Core (If you're seriously considering this I recommended torrenting the entire blockchain because it can take quite awhile to set up)
Pros
-Can be encrypted and kept safe
-Easy to access and use on a daily basis
-It is software so beware of fake wallets
Cons
-Can be a fake wallet and you can lose all your bitcoins
-Can be hacked if not encrypted or stored safely
Mobile Wallets Want to use your bitcoins on the go these wallets are for you ready on mobile and very compatible it is very useful for any bitcoiner.
-Mycelium

Pros
-Can be used in the go
-Less attractive to hack
-Easy use
Cons
-Not many options
Paper Wallets
Paper wallets are very intriguing to anyone new or old to bitcoins its kind of another physical way of saving your bitcoins most usually on a piece of paper as the name suggests. Paper wallets have to be made precisely as if your device gets compromised so can your bitcoins on that wallet, stay safe.
Thanks for reading

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Since this is very brief if you have any questions leave them below and I will look at them when I can and to the best of my ability.
Credits for help
-Bitkilo