I've used numerous of these over the years, but for presentations I always come back to the Kensingtons. There's two I used regularly - this one, and the older version of the same one that uses a "watch battery" rather than AAA. The watch battery version is better because it's smaller and fits in your hand better, but has the disadvantage that the battery is difficult to replace when it goes flat, whereas the new ones are AAA's which last longer and very easy to replace.

Both of these store the dongle inside the device, and the remote powers on or off when the dongle is removed/reinserted.

For a mouse, I do have a Targus wireless presenter with "cursor control" (ie, one of these, but it's really only good for very basic control over the mouse as it's slow and inaccurate to do anything meaningful. There are multiple newer versions that might be better, but I doubt it.

If I need to use a mouse I'll normally just use a real mouse (Logitech or MS wireless travel mice), or just use the computer directly.

Personally I'd avoid bluetooth, or things like phone-based remotes unless you know that you're only going to be using it on your own computer. I can plug any of my devices into any computer, and know that within a few seconds they are going to be working, without me even needing to touch the OS - that's not going to be the case for Bluetooth based devices!