Nano. Will it do what I want?

Hi Guys,
Oscilloscope noob here! I am doing some various tinkering that I think I could use an oscilloscope for and I am wondering if the DS201 will do what I need. I have a bunch of old Commodore 64s that I would like to try and fix so I would like to check that the clock outputs from the various chips are working. Will the Nano be ok for this?

My other project is I am trying to interface a six button Sega Megadrive controller to a Arduino Pro Micro using the sketch from here: [Cant add a URL apparently google Jon thysell megadrive revisited]
However it is only working in 3 button mode yet the controller appears to work ok with a real megadrive so I want to be able to look at and measure the sequences that are sent to the controller so I can emulate them exactly with the Arduino. The pulse widths are around 20 microsecs but could be less. So do you think the Nano 201 will be able to show me what the exactly series of pulses being generated by the Megadrive are?

Obviously these are just hobbies so I am not looking to spend a lot of money but if it isnt going to be able to do what I need then I will look elsewhere maybe a second hand something?

Thanks for the advice,

Edit: The Hantek 6022BE might be a better options perhaps?