Looking for something to run PS4/PC through

Get an AVR and some good speakers. There are good entry level AVRs from Yamaha (RX-V379), Denon (AVR-X1200W), Pioneer (Pioneer VSX-330-K) etc. for example. You´ll most likely be more happy with that than those crappy Logitech "systems". Just my 2 cents.

This is one of my favorite products for stereo application, especially at a desk. Basically every input you would need audio wise.

http/nadelectronics.com/products/digital-music/D-3020-Hybrid-Digital-Amplifier

If you want surround then you're basically bound to a receiver and they are generally cheaper too. Do you have speakers yet?

z906 is boomy, average quality. hifi speakers will blow them away but they arent bad for 'pc speakers'. you can do better but its certainly convenient how they have the inputs set up.

if you went with just a 2.0 system, a simple A/B switch would work (with powered speakers) although for ps4 use you might need to use the controller output or use an audio extractor device to get audio given the lack of analog out on the actual device. for pc use it will work fine as is. likely the easiest to find and set up without research although having two boxes is bulkier (but still smaller than a receiver by far).

a receiver also works but is a more expensive solution. you would be needing passive speakers not actives for that (non self powered). you dont want to try using one with powered speakers and its really too big of a solution for your needs.

another option would be if you find an external dac unit with two switchable inputs. you could use its analog low level output to some powered speakers. i know of some high end products that do this.. but i cant think of any cheaper ones (i'm sure they exist) that do this off the top of my head. this would eliminate a switchbox and extractor.