Side paddle steamers and rear paddle steamers were both very popular for river use. They combine power with a very shallow draft. You don't have to get the power down as deep as a propeller.
Reverse gear is very useful and can be done with a fairly primitive transmission. Many steamers landed on shore and would need to back up to get going again. Also if you go aground on a sandbar, reverse might be the best way off of it. Same mechanical principal as a train engine. It would have been one of the first developments to be implemented.
Speed would be controlled by a value that increases or decreases the steam pressure against the gear providing power. Decreased pressure would cause it to slow down and increasing the pressure would cause it to speed up. (Realize that "speed" here is a relative term. These suckers didn't go very fast.)
Control would be at the bridge. However, where it actually happens would be down in the engine room. You could use either a mechanical telegraph or voice tubes. The bridge would be where steering commands were also issued.
I'm not sure you need much more than the captain issuing an order down the voice tube to the engine room. Take a look at
https://en.wikipedia.org/wiki/Steamboat. It includes a picture of a model of a very primitive steamboat.
Jim Clark-Dawe