Real, quick, since you are new...
Quartz means it's an electronic watch that uses quartz to keep very VERY good time. These watches don't cost much because the technology is inexpensive.
The other major power type is "automatic," an old technology that uses the movement of your body to power the watch via some complex mechanics. "Automatic" watches are more desirable to "watch guys/girls" due to their complexity and awesomeness but they keep worse time than the cheaper "quartz" watches (they are often off by 2-3 seconds per day, and stop working if you don't wear them). If you want a good, cheap, accurate, watch you want quartz.
Quartz watches are either battery or solar powered. I recommend solar powered if you don't like trips to the jeweler or changing watch batteries.
Moving on...
G-Shocks (like you posted) are killer watches. Even "watch guys/girls" like me that turn their snobby nose up to quartz watches won't criticize a g-shock. They are meant to take a beating and the intricate mechanics of an automatic watch is a waste for that kind of use.
Now to my recommendations...
A cheap, $22, watch that I have and love is this solar quartz:
https://www.amazon.com/dp/B00791R1MI
I wear it to work out and to coach Soccer...so if it gets beaten up I don't care. Plus it's awesome to never have to change the battery.
You can just google Casio Solar Silver and see what options you like if you don't like my black choice.
Now, you pay a little extra for the solar technology, so the watches look a little cheaper. If you want something more baller looking, try something like this:
https://www.amazon.com/Casio-MTP4500D-1AV-Slide-Aviator-Stainless/dp/B00134OJYA/ ($55)
or
https://www.amazon.com/Casio-Quartz-Sport-Stainless-Silver-Tone/dp/B09HVB9RX8 ($79)
The only issue with those is you will need to replace the battery eventually. Not a big deal.
If you think you might want to try an "automatic" watch (no battery, no solar, doesn't keep great time, stops when you don't wear it, but still literally waaaaaay cooler than a quartz), you can start with something in this range:
https://www.amazon.com/Seiko-SNK607-Automatic-Black-Stainless/dp/B0012VR752
Look at the 3rd picture in the preview for that watch. It shows the back and exposes some of the super sexy components that make the watch automatic. Look at it and tell me it doesn't look sexy AF. If you don't care about those mechanics, you are going to save A TON on more accurate watches ;)
If you don't like my choices, there is a watch out there for you. Google "G-Shock style watches under $100" or something like that to see more options.
If you narrow down your choices and still have questions, just ask this sub. Lots of cool people here will help you out.
Good luck, and welcome to the world of watches. We all carry a cell phone that tells us the time 24/7, but you are one of the few that understands the importance of spending extra money on unnecessary, but awesome, hardware ;)
Yep, good news is it's a nice looking watch, bad news is that based on reviews it's not really fixable due to the way it's constructed, that plastic piece apparently doesn't hold up very well to removal. A jewelry place might be able to repair it though, might be worth asking at least.
If you do decide to buy a new watch I'd suggest something around the 50$ range. Usually they are bit a little better and the bands are easier to replace.
This is a decent one currently going for 43$ on Amazon and Walmart. Bestbuy also price matches Amazon prices :)
https://www.amazon.com/Casio-MTP4500D-1AV-Slide-Aviator-Stainless/dp/B00134OJYA