For bitcoin, I have used Electrum and so far this is the most trusted and safest wallet out there besides the Core wallet. However, Electrum is very fast and lightweight as well. You do not need to download the whole blockchain to be able to used it. And fees can be adjusted dynamically. So you have options to adjust it depending on your needs. And for your protection, you need to backup your seeds and private keys just in case something went awry on your laptop or PC.

For ETH - Jaxx wallet supports both ETH and BTC, however, there have been issues lately on Jaxx so I stop using it. I have tried MEW(MyEtherWallet) so far I haven't had anything bad to say about it. But just like any other wallet, backup is needed as well.