Myetherwallet COULDN'T decide transaction speed. It's safe if you know how to use it and make secure your coin.
MyEtherWallet (MEW) during use, more than a year, did not give me a reason to doubt its work. I open it through MetaMask. I do not keep the keys on my computer, as this is not safe. It helps in tracking transactions, bot telegram (ETH token Explorer)
ERC20:
@ETHtokenExplorer_bot
NEO blockchain:
@NEOTokenExplorer_BOT
For long and safe storage of your cryptomonet, use hardware wallets, such as: Ledger Nano S, TREZOR, Keep KEY.