The developer is simply a dilute alkali, I use 12g of NaOH in a litre of water. It's quite safe but don't get it in your eyes and wash it off if you get it on the skin. Ferric chloride is quite safe, just wash it off if it gets on the skin. I always wear rubber gloves, both for protection and so that I can use hot etchant with manual agitation (I put the etchant and board in a small container in an old washing-up bowl with about 1" of just boiled water in it).
I've been making my own PCBs at home for about 40 years, using ferric chloride mostly. The only accident I've had that could have been serious was when I was walking across the room with an open bottle of conc. HCl in my hand, tripped, and a little splashed on my face next to an eye. I thought it might have got in the eye, but the fumes were bad enough. I immediately put my face under a tap and flushed the eye out for several minutes. It was sore for a few hours, but there was no damage.
Well the most important thing is to actually think about everything you're about to do when connecting a circuit.
Check if the oscilloscope probe's ground pin is shorted to the power supply's ground pin (in most cases it will be). Check if output pins of the power supplies are connected to ground pin. They might be, but good quality supplies will have separate ground pin available on front. Also check if the PSU case if connected to ground (it probably will be) and if it is, take care not to have a positive wire touch it.
Every time you connect the scope to something powered by the power supply, think what's going to happen. I've seen cases where people shorted-out their power supplies using oscilloscope probe ground pin and couldn't realize why that happened.
Next, check how the power supplies are going to react in overcurrent situation. Is it going to shut down or will it drop voltage or something else? In general, familiarize yourself with equipment you'll be using.
Do keep in mind that a multimeter in current measurement mode is basically a short-circuit and in voltage mode is basically open circuit. Take care how you connect it! Do read the manual and try to understand what happens in other modes, if there are any. Take note of maximum voltage the multimeter can take with each of them.
For the end, once again, read the equipment manuals and try to plan out each situation in which you can find yourself in as far as the equipment is concerned and think about what will happen if you make a short somewhere.
ABOUT THE COMMENT:
The problem has to do with "floating" and "ground-referenced" power supplies. When a power supply is said to be floating, it means that you can't make a current loop which goes back to ground. An example of this is a battery-operated device. Current goes from one terminal of the battery to another and if you connect one side of the battery to the ground, no current will pass through the wire, because there isn't a closed loop for current to go through. Take a look at this simulation where the ground is connected to the positive output of the battery and no current goes through it.
Same thing happens when you have a transformer separating the mains side of a power supply from the low voltage side of the power supply. All current going out of the secondary side of the transformer needs to go back into the secondary side of the transformer and if you touch a wire along the path, no current should go through you since there isn't a loop for it to go through. Take a look at this simulation. Here too we have ground on the secondary side of the power supply and co current goes through it.
Now to get back to measurement instruments. A hand-held multimeter is often battery powered and is therefore isolated from the circuit it is measuring. This allows you to for example connect the negative probe of the multimeter to the positive pin of the power supply and positive probe of the multimeter to the negative pin of the power supply and the measurement will work, but you'll get negative voltage.
On the other hand, most oscilloscopes are connected to mains power and the ground pin of the probe will usually be connected to the ground pin of the oscilloscope's power supply. On some bench-top power supplies, the negative side of the secondary is connected (or can be connected) to ground. If you for some reason connect the ground pin of the scope probe to the positive pin of the power supply, you can create a short. It will look something like this.
This device is an intentional radiator (it transmits RF) so it will be relatively expensive to get it certified for all jurisdictions. Safety is on top of that.
Your product may be otherwise well designed with what you think are good protections, but if a single-point failure can cause a fire or electrical shock then it may need to be modified. If every part that comes near the mains is plastered with listings and your design is decent it will be a lot easier/faster/cheaper. They don't care so much if your product is reliable or useful, the focus is solely on whether it can cause harm in one of a number of ways. For example, the plastic housing may need to be made of an appropriate resin with fire retardant additives to be approved, but certain fire retardant additives are banned in some jurisdictions.
So maybe decide where you want to try selling it and research which standards apply (often there are gray areas) and get ahold of copies of the relevant standards.