Is it good to just buy BTC & ETH @ Coinbase and leave it there for investment?
I think the fees might be pretty high or is it not?
And after I buy it, should I leave it there or send to some of my created wallets in Electrum for example?
Yes it is Ok to buy their since coinbase is pretty more known exchanger where you can buy both of coins you've mentioned and also you can buy at localbitcoin but i don't know if they had ETH handle on their. An as I See you want to buy for staking sake well electrum is quitely reputable wallet but take proper precaution since anything can turn bad these days and use hardware wallet instead if you want to stake huge volume of that coin.