You might want to play a bit with BIP39 , BIP44... : These are protocols that can generate private keys and public keys multiple ones for multiple coins and are easy to backup. Even hardware wallets use these protocols and many mutli-coin wallets. Also I use it as it is easier to backup many alts in one place- can be used as offline wallet.
Basically you can enter your own words or simply generate random words write them down, keep them in your head etc. save somewhere few public addresses to receive coins and you are good to go. When you need to send coins you will need to reveal private key.
If you are interested in how they work:
https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki
https://github.com/bitcoin/bips/blob/master/bip-0044.mediawiki
You can go here: https://iancoleman.io/bip39/ , right click page go to "Save page as" so you can put it on USB or some other devices to be able to run offline. For offline running I'd suggest you use some live OS such as Ubuntu or any other without connecting to the internet. Live Operating Systems runs only in your RAM memory which means that when you shut it down it leaves no trace on your computer you can have access to your computer files where you can simply save your public addresses.
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paper wallet generator (advised to run offline on live OS and print keys): https://walletgenerator.net/#
This video really sums up what are priv keys and public addresses, security of them etc. it will give you basic understanding - really well documented if you have like 30mins I'd recommend you to take a look: https://www.youtube.com/watch?v=I1uefzJJ6nM
Hot wallets vs cold wallets = https://www.youtube.com/watch?v=Aji_E9sw0AE
Multi coin wallets
These are not considered as secured ones as the ykeep private keys on your computer in encrypted/unencrypted form. It's not good if some malware gets on your computer
Here are to name few: coinomi(android), exodus(desktop) , jaxx (mutli-platform)
Hardware wallets : https://en.bitcoin.it/wiki/Hardware_wallet
ASK ANYTHING THAT YOU DON'T UNDERSTAND!
P.S. Transaction fee doesn't have to do anything with which wallet you use, some of them have strict fee and some don't in case of software/hardware wallets. In short fee is set by the network itself.