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
Get whatever meets your needs for voltage, current, readouts, size, price, etc. Don't worry about whether it is a switcher or linear.
In general, linears are less efficient. However, this matters little to a bench supply. The few watts or even 10s of watts it might occasionally draw more than the equivalent switcher is irrelevant. It will get hotter, but presumably since you are buying a whole box this has been designed in. Unless perhaps you have a very specific physical spot in mind for this box and there is little room for ventillation, the extra heat of a linear won't matter.
Switchers will have some switching noise on their output. Again, this shouldn't matter. Check the ripple spec, but the ripple of any finished-box commercial lab supply really shouldn't be that high, a few 10s of mV at most.
What exactly is the problem with ripple? Not much in a bench setting. Things like relays, motors, LEDs and even the occasional LEB (light emitting bulb) aren't going to care. But the most important point is that a well designed circuit should be fairly immune to power supply ripple. If your circuit can't handle a few 10s of mV of supply ripple, what's it going to do when it gets off the bench? In the few cases where supply ripple might matter, you should get into the habit of adding the appropriate filters anyway. For example, to power the opamp for the sensitive input circuit of a microphone preamp, put a ferrite chip inductor in series followed by maybe a 10 µF cap to ground feeding the opamp power pin. Other places may need a bit of filtering too, but that's something you should be doing anyway. Using the microphone amp as a example again, the final stage may draw enough power so that it makes its own "ripple" on your local supply, whether the original power supply was perfectly clean or not. This is just normal design practise.
So all this is a long way of saying don't worry about it. There are even hybrid types where a switcher does most of the work with a linear post-regulator that only drops half a volt or so to clean up the noise or let you get down to low currents and voltages nicely (which some switchers have a hard time with). Again though, you are buying the overall box. Look at what it does as a black box and don't worry how exactly all the specs were accomplished.