Ok, learning something here. I have a noisy environment.
All of the following is done with AC channel coupling.
Turns out that about smallest increment I can discern with just the Rigol scope turned on is about 250-500 microVolts. That is, with nothing plugged in and the channel on the signal displayed on the screen with it's attendant noise is about 250-500 microVolts. When I plug in a Tektronix BNC cable (about 30" long) nothing changes on the scope signal - it is still approaching 500 microVolts. When I add a BNC to banana plug connector (so the banana plugs can plug into the Power Supply) the signal jumps to a range of 2.5 milliVolts to 5 milliVolts depending on the orientation of the cable with the connector (it seems to act as an antenna).
When I plug the BNC cable from the scope through the BNC to banana plug connector into the Power Supply (with the Power Supply OFF and it's AC cord disconnected from the PS), the signal settles down to show about 2.5 milliVolts at it's "core" but the nose emanating from the top and bottom of the "core" of the signal takes the signal to about 7.5 milliVolts peak to peak. Plugging the AC cord into the wall and into the PS doesn't have any impact on the signal amplitude.
When I turn the PS on to 5 Volts (with no load), the signal rises to 5 Volts and looks clean but when I zoom in by setting the scope to 5 mV it becomes apparent that the signal has a "core" component that is about 2.5 mV and the noise takes the overall signal to about 7.5 mV peak to peak - this is with no load.
When I turn the PS off, attach the load to the PS, and attach the scope to the PS I get a signal of about 8.3 mV peak to peak. When I turn the PS on, I get the image below which shows what I refer to as the "core" of the signal being about a third of the overall signal which measures with the cursors as being about 9 mV peak to peak.
How much of the 9 mV is due to the PS and how much is noise from cables, connectors, or all of the above acting as an antenna I don't know but after working my way through this I am thinking that some of it is noise from the environment. I have found that depending on how I orient cables and connectors and how I hold them can have a dramatic impact (10x?) on the noise level.
So, my assessment so far is that the Tekpower TP1503C has relatively little overshoot on turn on and turn off (see the earlier images posted) and it might be about 3 mV for ripple. I can't say for sure given my adhoc technique and what I think is a noisy setup and/or environment.
Over thoughts: I like having a PS with analog meters but I wouldn't want it to be my only PS. If I only had one PS there is no doubt it would be worth the extra $ to have digital readouts for Volts and Amps, but all in all if someone needs a PS for $40 the Tekpower TP1503C seems like a reasonable starter unit (but I'd still hold out for digital readouts if you can).