OK so I've gathered that you need something to produce sound at a sub $200 price point. You really should be looking into an AVR with some speakers to do this right. However, that being said your $200 price limit is going to be hard to do that. So let's move on toward the soundbars.
What you need to do is identify the sources that you are wanting to put through your sound system. So far we have TV, Computer, Keyboard...anything else that is missing?
Most soundbars only have about two to three inputs on a good day. You're already maxing out the inputs with what you have listed and depending on what kind of input you need you might be switching them out unless you get a switching device. I'm assuming the TV has just a cable hook up to the schools system so you're probably going to use the optical output of the TV into the soundbar. That leaves you with the digital coax and analog input/s left. You can use the headphone out of the laptop to get signal into the soundbar but that will be stereo. Not the biggest drawback as most soundbars are not 5.1 in your price range. This leaves maybe one analog input left or the digital coax if the model you choose has these. Depending on the keyboard output you might be ok but you might not.
I'm thinking you're going to need a switch unless you want to keep unplugging and plugging in inputs. If your laptop has optical out for audio I would get something like this to switch the tv and laptop output into the soundbar.
Ok so now the next question do you want to have 5.1 or just go a 2.1 route? I would go the 2.1 for the cost savings and simplicity. The fact that you're putting this in a bedroom also factors into that decision. I did say 2.1 which means you should look for a unit with a sub of some kind. Sub meaning probably more of a mid bass unit as most of the drivers will be in the 5-6" range for these units. Either way you're going to want one for the low end fill.
Here are some examples I would look at if I were you:
If you have questions let me know I'll try my best to answer them.