You have the right idea for a basic unregulated supply. A transformer, four diodes, and as large a cap as you can manage will serve well enough for a lot of purposes, but isn't appropriate for all.
There are two main problems with such a unregulated supply. First, the voltage is not known well. Even with ideal components, so that the AC coming out of the transformer is a fixed fraction of the AC going in, you still have variations in that AC input. Wall power can vary by around 10%, and that's without considering unusual situations like brownouts. Then you have the impedance of the transformer. As you draw current, the output voltage of the transformer will drop.
Second, there will be ripple, possibly quite significant ripple. That cap is charged twice per line cycle, or every 8.3 ms. In between the line peaks, the cap is supplying the output current. This decreases the voltage on the cap. The only way to decrease this ripple in this type of design is to use a bigger cap or draw less current.
And don't even think about power factor. The power factor a full wave bridge presents to the AC line is "not nice". The transformer will smooth that out a little, but you will still have a crappy power factor regardless of what the load does. Fortunately, power factor is of little concern for something like a bench supply. Your refrigerator probably treats the power line worse than your bench supply ever will. Don't worry about it.
Some things you can't do with this supply is run a anything that has a tight voltage tolerance. For example, many digital devices will want 5.0 V or 3.3 V ± 10%. You're supply won't be able to do that. What you should probably do is aim for 7.5 V lowest possible output under load, with the lowest valid line voltage in, and at the bottom of the ripples. If you can guarantee that, you can use a 7805 regulator to make a nice and clean 5 V suitable for digital circuits.
Note that after you account for all the reasons the supply voltage might drop, that the nominal output voltage may well be several volts higher. If so, keep the dissipation of the regulator in mind. For example, if the nominal supply output is 9 V, then the regulator will drop 4 V. That 4 V times the current is the power that will heat the regulator. For example, if this is powering a digital circuit that draws 200 mA, then the dissipation in the regulator will be 4V x 200mA = 800mW. That's will get a 7805 in free air quite hot, but it will probably still be OK. Fortunately, 7805 regulators contain a thermal shutdown circuit, so they will just shut off the output for a while instead of allowing themselves to get cooked.
BK Precision 1550
This is a switching supply.
The up-down adjustments would make this a non-starter for me.
CSI3005X5
A whole bunch of companies re-brand this unit. They're actually fairly decent. The voltage pot is a 10 turn, the current limit is button-driven in 0.03A increments.
The most common resaler of the power-supply is MPJA. It also comes in a bunch of voltage and current ranges: 0-30V 5A, 0-60V 3A, 0-120V 1A.
One thing you can't see in the pictures is that the unit has a set of screw terminals in parallel with the output banana jacks, below the cover plate labeled "EXT OUTPUT". If you need more permanent connections, you can use the screw terminals.
The schematic for the whole supply is available. This makes it enormously more repairable (and hackable) then ANY of the others.
BK Precision 1671A
The funky extra output connections on this make me nervous (speaker terminals? really?).
I would guess that the potentiometers are single-turn, both from the artwork on the case near the knobs, and the fact that it does not mention multi-turn knobs, as that's normally a significant selling point at this price range.
On the whole, If I had to choose from the supplies listed, I would wholeheartedly recommend the CSI3005X5, more because the alternatives are considerably worse.
Anyways, I would say that even if you don't think you need a floating output power supply (what you really mean when you discuss a separate earth terminal), you almost certainly will find it useful in the future, so I think you shouldn't dismiss it. Just being able to string multiple power supplies in series for higher output voltages is tremendously useful.
Best Answer
Since you're using a linear post-regulator after a switcher, the switcher can afford to have more ripple than you want on the output. This allows for very simple control schemes for the switcher.
I haven't really thought this thru carefully, but my first knee jerk reaction is to do a fairly dumb switcher in the micro. Possibly the firmware doesn't even get envolved with the switcher control once the PWM generator is set up.
The micro would take care of the user interface, reading the voltage and current setpoint knobs, getting commands from a communication interface, displaying values, etc. It then creates the reference voltage via PWM, which is low pass filtered and presented to the analog section. Likewise, it makes a current limit setpoint voltage.
The voltage controller is a simple opamp with FET follower. A PNP transistor is used to detect the switcher output being 700 mV or so above the actual output. This produces a binary signal that drives the shutdown input of the PWM generator in the micro.
The current loop is a high side current sense between the switcher and the output FET. A ground-referenced current-magnitude signal is created, which is compared to the filtered current limit voltage from the micro. A comparator is used to also shut down the PWM generator when the current is above the setpoint.
For extra credit, have the micro continually read the raw input voltage. It then adjusts the PWM duty cycle for the optimum value based on the input voltage, the output voltage setpoint, and the maximum current that the switcher needs to be able to deliver. This dynamically tweaks the efficiency a bit, and should help avoid inductor saturation.
This scheme of fixed PWM with shutdown will cause more ripple on the switcher output, but since that's followed by a linear regulator, it shouldn't matter much. The big advantages of this method are that it is very simple, and inherently stable over the wide range over operating points a bench supply must be able to handle.