Not sure what to check first. Wiper motor? The computer (which, I feel like I would not be able to do on my own).
Wipers have been responsive every time I go to turn it on, however, while in use, only sometimes, it starts to go faster. If I have it at a lower speed, it'll go, but then it'll randomly start to go the faster speed, and when I try to switch it off completely, while its "spazing" out, it'll take a bit for it to stop. Sometimes too, when it doesn't spaz out and I just go to turn it off regularly, it randomly speeds up a little and takes a little bit for it to stop.
This does not happen with the rear. The rear has been steady, but I know it's a different motor.
I don't want this to become an issue of not coming on when needed, so I want to try figure out what it could be now.
Any guidance is appreciated!

 

When I read your question, my immediate thought was a problem with the wiper switch or a faulty/intermittent ground.
I then read a few of the "Related Posts" below your question, which I would suggest you do as well.
Seems like a number of folks have had issues similar to yours caused by moisture, dirt, or other debris in the wiper motor connectors under the cowl, so I would probably start by checking those connections.