The only type of oscilloscope that won't be able to display a non-periodic waveform is a "sampling" type (which are now referred to as "equivalent time sampling" to distinguish them from ordinary real-time sampling digital oscilloscopes), and that type is mostly used at frequencies where real-time sampling is difficult (GHz).
Even a cheap digital oscilloscope samples fast enough to see a snapshot of a signal with a bandwidth of 50MHz or 100MHz in a single shot (0.5G samples per second is common in inexpensive scopes).
It perhaps needs to be mentioned that the oscilloscope will only have a certain "depth" of memory so you will only get a kind of keyhole view of the signal, starting at the trigger and extended some thousands of samples after the trigger. After that snapshot, the oscilloscope may trigger again or it may not, depending on how you've set it up, but you cannot gather true continuous data from the input with a typical oscilloscope, just snapshots of it.
For continuous acquisition (say to capture the signal over many seconds, minutes or hours) you need a data acquisition system capable of taking samples at at least double the highest frequency component of interest, and of sufficient bit width for the accuracy you care about, and storing it to suitably capacious memory in real time. It's not hard to fill gigabytes of memory if you're gathering high precision data over multiple channels.
The 465B has two time base, A and B. The B time base is called delayed time base and can be used to zoom on a portion of a signal to see it in greater details. You can also trigger on this zoomed signal by using the trigger B (and the "DLY" is for "delayed" or "delay").
You can watch some videos from w2aew on youtube here. He has differents tutorials on Tektronix oscilloscopes.
Best Answer
There are two 'ground' points in play here:
Earth ground is for safety. Connect to earth ground if you like.
Signal ground is for measurement. Connect to a ground on the circuit you are testing. Preferably something near the signals you want to probe.
The signal input of the scope has two front panel BNC connectors for probes. When you connect the probes, the center pin of the BNC carries the signal you are probing, while the outer ring of the BNC carries the signal ground.
If you are probing a digital circuit, for instance, you'd want to connect the signal ground to whatever ground all the digital logic uses.