According to the User Manual, with a 10x probe, the maximum input is still 300V (3,000V at the probe) and CAT II.
So, from a voltage point of view, I would just use a 10x probe and realize the scope is only seeing 7.2VDC. IF the probe got inadvertently set to 1x, no big deal, the input to the scope would be 72V, well below the 300V limit. But I almost always use 10X. If I were truly paranoid, I would buy a 100X fixed attenuation probe. No switches...
There is nothing to see on the output of the transformer that won't show up on the output of the rectifiers so why bother?
As long as your supply is EXACTLY as drawn with no hidden earth ground connections, you should be good to go on the DC side. You will be effectively grounding the negative side (and there's doesn't seem to be a reason this won't work) when you connect the ground clip. But you could ground the negative rail anyway and, in fact, you could do that with a piece of wire before you even begin probing. If you do that, you absolutely don't want the the transformer secondary grounded.
If you simply must look at the transformer (and I can't think of a single good reason for doing that given that the rectifier output is correct), remove any earth grounds that may exist on the DC rails and ground one side of the transformer secondary. This will be where you place the probe ground clip.
Basically, you don't want the scope to be providing an earth ground to anything. It is far better if you have already grounded a DC rail or transformer secondary lead external to the measurement process. This will eliminate potential arcs, sparks and smoked scopes. BTW, if you do apply an external ground to the DC (-) rail, you probably don't need to use the scope ground clip. The image will be close enough just using the probe tip and the fact that the scope is already grounded.
I don't know what you expect to see. It doesn't seem like the kind of supply where mV of ripple are going to be a factor.
BTW, when you are looking at the DC link and you want to see ripple, choose AC Coupling and reduce V/Div so you can see the ripple riding on the DC.
Dave did a video:
It's a best seller...