Checking on your main speakers, it looks like they use 8cm drivers which converts to about 3-1/2".
The sub had an 8" driver.
Did you sub have a knob/control for the crossover frequency? I am guessing not (based on the following info). If it does then ignore this
The sub specifications indicate "High frequency cut off frequency is 150Hz".
I would expect this is what is more traditionally called a Low Pass Filter fixed at 150Hz, so that is the place to set the crossover frequency.
So the sub you get should have a knob for the crossover frequency that allows you to set it at 150Hz (some subs have lower values for their max crossover frequency).
This one is $80 shipped and Monoprice does a good job with their budget subs (I would expect this to out perform the original Sony sub):
https://www.amazon.com/Monoprice-108248-60-Watt-Powered-Subwoofer/dp/B009GUTJ34/ref=sr_1_29?keywords=8"+subwoofer&qid=1568810368&rnid=493964&s=electronics&sr=1-29
Ideally you will stumble across a used one that would do the job for $40 or less. There are many subs (as I believe to be the case with yours) that were part of a package and
do not have a control for crossover. No guarantees, but 150Hz does seem a common crossover frequency for these package setups (which typically come with smaller "satellite" speakers like yours with the 3.5" drivers). If you run into one of these at your local thrift shop for $10, it may be worth a gamble.
My approach for setting the volume for a sub in a system like this is to play music I am familiar with that has a good bass line and gradually increase the volume on the subwoofer until it starts to be obvious that sounds are coming from the sub (IOW, you will hear the fullness of bass in your room before you distinguish specific sounds distinctly coming from the subwoofer). Stop here - I usually find this is a very good starting place. Go back to your listening position and see if you want more or less bass. From the listening position, I generally don't want to hear anything coming distinctly from the sub (I presume your ears were much closer to the sub when you were adjusting the volume),but I do want to hear fullness in the bass region.