The Logitech R400 has been around for a while, it's a solid, affordable presenter (with a slightly crappy laser, though) and you can get a good deal for it online.
To have it fully work with a PDF presentation on Okular - i.e. use all four buttons - I had to do some simple tweaks.
First, find out what the buttons do by running xev in a terminal.
(1) and (2) are mapped on 'Prior' and 'Next' and work out of the box. (3) is supposed to toggle presentation mode and alternates between F5 and Escape. (4) is meant to toggle a black screen and transmits a period, '.'
The quickest fix is to just redefine Okular's keyboard shortcuts in the Settings menu. I set the alternate shortcut for 'Switch Blackscreen Mode' to '.' and the one for Presentation to F5. Note that this disables the default 'Reload' shortcut, but Okular usually reloads automatically, so it's not too bad.
The alternative is to remap the presenter input from F5 to eg. F4, which is not conflicting with Okular's default scheme. I googled a bit (see this handy Medium post) and found input-remapper, which is in the Ubuntu repos and comes with a polished and quite self-explanatory GUI.