I agree with others that switchers are a better choice in terms of efficiency, but they can be somewhat complicated to deal with if you're inexperienced, and there can be lots of weird effects that aren't immediately obvious (precharge sinking, beat frequencies, etc.) that can make life difficult. Assuming you've figured out your power dissipation and know how much current each rail can deliver, if the linears will work for you, stick with them (at least for the first pass).
If you're trying to achieve a variable-amplitude square wave output on your adjustable rail, the chopping may introduce noise into the main 24V rail, which could show up on the other rails. You may want to have an LC filter between the main 24V rail and the regulator input to provide high-frequency isolation, and will probably need extra capacitance on the adjustable regulator output (bulk electrolytic as well as low-impedance ceramic) if you expect the square wave edges to be sharp.
1, 5) There are some dangers with your scheme.
Power dissipation in the linear regulators will be
\$(V_{out} - V_{in}) \cdot I_{out} \$
which is significant, especially for the lower output rails. 78xx-type regulators have built-in thermal protection around 125°C, and (without heatsinking) a junction-to-air thermal resistance of 65°C/W. Your thermal management will be challenging.
Another potential problem - if the series-pass element in any of your low-voltage regulators fails or gets bypassed (shorted), you'll present the full 24V input to the output. This could be catastrophic to low-voltage logic. You should protect your low-voltage rails with SCR crowbars that can sink enough current to put the DC/DC brick into current limit and collapse the 24V rail (they'll need big heatsinks too). Fuses are unlikely to be good protection since the 24V brick likely isn't stiff enough to generate the \$I^2 \cdot t\$ needed to blow a fuse.
2) Whatever floats your boat.
4) Meters aren't huge loads. Just use one of your rails.
3) Correct - all regulators have headroom requirements. If you want the maximum 24V out, you'll need a direct connection, and will have to rely on whatever intrinsic protections the brick will provide you.
In principle, what you want to do will work. But as you say, it's a matter of risk and peace of mind. It is possible, though unlikely, that the unit you are considering (and widely available for almost nothing on ebay) could fail in such a way as to deliver a damaging voltage to the camera, which would be expensive to fix.
The main situation to avoid is over voltage. To avoid that you could add a crowbar circuit (see google if interested), but that seems like work.
The other issue is whether or not the camera presents a highly variable load, as Dave suggests. In that case the 3A rating on the ACK-E6 may be an average that doesn't represent the peak required, which the capacitors on your regulator board may not be sufficient to supply.
A possible workaround for both these problems is to take your existing ACK-E6 and interpose a connector between the brick and the "battery" block. Connect the brick for mains power, and instead connect your DC-DC converter (set to 8V I think from the spec) for alternate power. The ACK-E6 spec suggests that there's some active regulation in the "battery" block, and that would help moderate any over-voltage accident, and I would expect provide sufficient capacitance to handle transient demand.
But all of this is somewhat speculative without schematics!
Best Answer
Use full wave rectification, not half wave. HW uses transformer poorly, may not be good or TEC, has no obvious advantages except the cost of 3 diodes.
If you want to operate it at full power with no control of cooling level then 12V is fine. LM350 regulator needs about 3V headroom. So 12V out from regulator = 15VDC in min.
Full wave rectified transformer will give ABOUT Vmax DC ~= 1.4 x AC voltage.
Or VAC_min ~= (Vdc + dropout) / 1.4 So 12V + 3V = 15V
VACmin ~~~~= (12 + 3) / 1.4 =~ 11 VAC if ~= NO ripple voltage ie 12 VAC transformer will give 12 VDC after regulator if well smoothed.
More is better, so maybe 14 VAC - 15VAC will allow regulator headroom plus some ripple allowance.
If all you want is to run it at full power then a transformer, bridge rectifier, smoothing capacitor and series resistor are all that is needed. Resistor drops excess voltage. A 10 VAC transformer will be about enough (1-VAC x 1.4 = 14 V with smoothing and ripple) and 12 VAC will definitely be enough. Resistor dissipates 2.5 Watts per volt of drop. A length of Nichrome wire adjusted to provide correct voltage to Peltier is one option or 0.4 Ohms per volt of drop select-on-test.
Regulator WILL need heat sink - how much depends on transformer. At say 3V regulator drop - about the minimum you should figure on, the dissipation V x I = 3V x 2.5A = 7.5W. Say allow 10 Watts. More if transformer is of excessive Voltage.
Heatsink can be selected using degree C (or K) per Watt for commercial heatsinks. For a 10C rise at 10 Watts you need 1 C/W heatsink which is "very large indeed".
If you want heatsink at almost cool enough to touch (almost) say 60 C the if ambient = 30 C worst case heasting delta T = 60-30 = 30C so heatsink = 30C/10W = 3 C/W
Even that is largish. Going other way, 10C/W is common so 10 W = 10W x 10 C/w rise = 100C./ Add ambient + Tsink = 100C rise + 30C = 130 C.
You rally don't want 130 C heatsinks.
so somewhere between 3 C/w and 10 C/W leaning towards 3 C/W end.
Fans and Peltier together are OK. Fan load is small compared to Peltier load.
Fans could run from smoothed DC before regulator - maybe with a dropping resistor of their own suited to VFan an Vdc.
Strip board construction OK but keep wires short and heavy. If running higher currents along a piece of stripboard you can solder wire to the strip for longer high current leads or use a wire link from points to be joined.
Main mains caution is DON'T PLAY WITH MAINS whn not needed. eg here all the circuitry is LV apart from mains feed to transformer primary. Do the primary side wiring well. Insulate as required. Then leave it alone.