While cottered cranks do have their drawbacks, there's little-to-no actual benefits from replacing them as long as they're still OK.
And bent cranks do happen, but IME bent pedals are more common. They'll both feel the same while riding, so figuring out which is which usually requires a good eye. And as you thought it "rode nice" before, replacing that isn't an immediate concern.
A crank upgrade/update can be quite a challenge for the unwary, you need to figure out exactly what type of bottom bracket the bike uses. There are a several versions to choose from.
For gears what makes most sense is an internally geared rear hub. I'd look for a complete wheel, either buying if done, or having one built for me. Changing from old 3-speed to new 3-speed is rather pointless, unless the old is broken. Changing to a newer 5-speed or more may make more sense. Going higher, you might find the build awkward due to the relatively small wheel size and the size of the hub.
Chain guard - can't help w/o pics. There's usually one screw by the chainstay, one by the seat tube, and one, on a bracket extending down from the Bottom bracket shell.