The best and most secure way to get and app is through the developer’s website. Many developers offers direct download or purchase (in case of commercial apps) of their apps. An example of commercial apps you can buy out of the play store is the very good aqua mail, or sygic navigation.
Moreover in this way you give 100% of your support to the developer and are not forced to pay the obscene 30% google tax.
I would never ever trust any online apk downloader which may temper legit apps including malware and the likes. If you want to go that way, use a pc installed apk downloader like GooglePlayDownloader for linux (which is an open source application and therefore you can trust it’s not doing anything evil).
Lastly, as may already said, F-Droid is an excellent source of free and legit apps.
Remember that going away from Google gave you may advantages, but weakened a bit your mobile phone security. If you know what you’re doing there’ll be no problems, but you must be a bit more careful about what to install and trust.