Thanks for all the replies!
It seems that a hardware wallet pops up a lot over and over so it seems thats the direction that I need to go. Why is MEW so highly regarded? Are there no other wallets that are considered as highly as MEW?
You can also check Mist, many people consider it is a better wallet than MEW. And there are plenty other wallets for Ethereum, but I suggest you to use a well known one (at least until you become more familiarized with this crypto thing).
I`m using MEW since the beginning and I never had problems - first I used it with Json and password, then I found out it`s more secure with Metamask so I added it and now I`m using MEW together with a Nano S (by the way, the Ledger stores many other coins, not only ETH and its ERC20 - Bitcoin, NEO, Ripple, Litecoin, Dash etc). Ledger or Trezor, it`s up to you, but a hardware wallet is a must!