For $40 you can get a FNIRSI DSO152 battery powered single-channel pocket oscilloscope. It only has one screen of storage, and is _very_ basic, but it's usable for simple diagnostics where a multimeter isn't sufficient. For old Volvo examples, google: "Automotive Diagnostics with a Cheap Handheld Oscilloscope"
The next step up would be one of the 2-channel handheld overgrown-multimeter style scopes, e.g. Owon HDS242, for ~$120. They have a few screens of memory and better triggering.
For ~$200, you can get a 2-channel 2000 series picoscope (which you need to mate with your laptop PC) that has minimal storage, but has a special mode that:
"The lower cost / bandwidth PicoScope 2000A models have smaller internal memories but when sampling at rates of less than 1 MS/s use USB streaming and PC memory to provide a 100 million sample buffer."
The 2000B series, starting at ~$450, have internal deep storage.
The automotive picoscope series are nice because they give you access to picoscope's automotive waveform library. The cheaper non-automotive series don't include this.
Both Rigol and Siglent have entry-level benchtop oscilloscopes with a ~7" touchscreen, lots of features and deep memory for ~$350, e.g. DHO802 / SDS802X. They're sort of fragile for the automotive under-the-hood environment, and are more difficult to learn due to all the features.
For the current clamp, you can buy a $75 Hantek AC/DC clamp and use it with any oscilloscope. It puts out a small voltage proportional to the measured current. On basic non-automotive scopes, you'll need to do the translation from displayed volts to current yourself, e.g. 1mV on the display means 10mA of current. The automotive scopes allow you to pick a probe type of: amp clamp, and will display the trace units in Amps.