It's been awhile since I've used it but Moon+ Reader on Android can sync progress to google drive. At the time the syncing wasn't super reliable, but it worked sometimes.
It supports Support epub, pdf, mobi, chm, cbr, cbz, umd, fb2, txt, html, rar, zip or OPDS
Its nicely customizable, takes up the whole screen when running including status area, has a night mode, can autorotate or pin the orientation.
Personally I really like using it plus calibre companion to sync files with my computer.