For about 3 years I've been using a wallet that is given for free with Localbitcoins account. I don't keep large amount in it, yet for small amounts it is awesome. Fees for outgoing transactions are small, just now - 0.00003462 btc. There is a fee for incoming transaction though - 0.00010386 btc currently. The wallet is good if want to but and sell bitcoin on the platform. Localbitcoins platform works since 2013 earn money from sellers commission so they are incentivized to keep user accounts safe. Never had an issue with them.

I also used a wallet on Blockchain.com for years with no problem. Although this wallet is the oldest and very popular, so there are many fishing sites and phishing e-mails, you have to be careful and always check url address in the browser. 2FA use is a must as well.