Since this is a pretty complex ana-digi movement I would only clean it if it is dirty on the inside (which is usually unlikely).
For the most part you're only going to have to clean the inner keyless works where all the metallic non-electric parts are (the ones that turn the hands) and lubricate them. Anything that is electrical just use an air blowing tool and lightly clean them (especially the contacts) with something soft, maybe a soft brush.
You have to take it all apart to reach the area where the gears/wheels are. You'd need some special grease and oil for them. Usually they use quartz watch oil. Can't remember what I used specifically.
Welcome to the forum!
What you're playing with is basically the most sensitive part of the watch.... I think you're better off starting over from scratch, buying cheap movements to practice on, all the tools you needs, and then, try to fix the mess. We're talking at least a few months worth of practice here.
Or you can take it to a pro who will fix it for you, but we're probably talking many 100s of dollars at this point... (a proper cleaning of a working watch would have cost a couple 100s maybe)
It is a nice watch, it's a shame it got all mangled up. If you do decide to take on this hobby, watch all the videos, ask questions, take it slow. In a few months, you'll be very proud to have a working watch again (just make sure you break a few cheap ones first).
I serviced a watch like yours a few months ago. Mine had somewhat similar issues with the seconds hand. I just cleaned the movement, lubricated it and then assembled it back together.
You'll find a few videos made by someone on how to take that movement apart on youtube but they're not very good if you don't have any experience.
If you don't have experience with working on watches and if you don't have the right tools I suggest you take it to a watchmaker or leave it alone until you get more experience (if you're planning on doing this as a hobby or something).