Wow tube tester. Haven’t seen one of those in ages. Used to be everywhere.

 

So, does the software scope detect different wave shapes or it just reads the peaks and assumes it's a sine?

Also, is there other gear I might need? I've also heard about logic analyzers?

Software uses hardware. If you are talking about sound card scope, then sound chip digitizes the incoming signal and that is what software shows to you. However! Remember that sound chip has a sampling rate that is designed for human speech (or reproducing human speech), so the maximum sampling rate is 40-48 kHz. The 40-48 kHz sampling rate tells you that this sound chip is designed to sample 20-24 kHz frequencies. Now look ahead a little. You said something about radio. How much of the radio you are thinking about is in 0-24 kHz range?

Just for general education. Human audio is from about 2 Hz to 20 kHz. Nyquist Sampling Theorem tells us that our equipment must have sampling frequency that is two times the frequency of the signal that is being sampled. So. Maximum frequency for human audio is 20 kHz, to sample it properly you need 2*20 kHz=40 kHz or better equipment. That is why they stick 40-48 kHz audio chips into computers/audio cards.

My issue with sound card scopes is that audio inputs are designed for microphones that produce a few millivolts. You feed it 5V from Uno board and you will destroy the input stage of the sound chip. If I am wrong, let me know (I am honestly too lazy just now to google it). I have old portable HP scope that I got on estate sale and I got fancier Tektronix scope off ebay, I think I am set for life.

OP. For you I would seriously consider something like Analog Discovery unit, watch the videos, here is the first one:

 

Wow tube tester. Haven’t seen one of those in ages. Used to be everywhere.

The world went to hell when they took the penny scales and tube testers out of the drugstores.

 

The world went to hell when they took the penny scales and tube testers out of the drugstores.

Yeah I had to buy a Mil Surplus one at a Ham Fest for my old tube transceiver Heathkit HW-101 after that. Now it's buried somewhere out in the garage.