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.
Answers to 1 and 2 should come mostly from the datasheet of whatever switching power supply chip you plan to use. First you have to make sure the chip is intended for your input voltage, output voltage, and maximum current. After that you need to follow the directions, carefully.
These kinds of chips are designed assuming a certain range of parts external to them. The datasheet will tell you what is acceptable and it may even give you some guidance what values to use over a range of parameters. For example, the datasheet might recommend a larger inductor for the upper half of the input voltage range. However, you'll probably pick a chip because it's max characteristics exceed your requirements by some reasonable margin. In that case, you follow the recommendations for the max case, since that's effectively what you will be using. Some datasheets assume this and only give you one set of recommended values. Just follow them.
As for question 3, yes, switching power supplies can cause more EMI. The main trick is to keep all the local loop currents localized to the power supply sub-circuit, and to keep these loops physically small. This means starting with a good layout, then carefully routing the key nets. Make a separate local ground net for the switcher, then tie that to the main ground in only one place, probably right at the ground side of the output capacitor. This keeps the loop current thru the diode, inductor, and output cap localized and off your main ground plane. Only the net delivered current should flow thru the power and ground feed points from the power supply sub-section.
Best Answer
One way to start on this would be one of the free power design simulators provided on various manufacturer web sites.
Since you mention Texas Instruments, try their WeBench Power Designer and SwitcherPro Design Tool.
While familiarizing yourself with these tools, you will understand the additional parameters that need to be defined for optimal selection of regulator.
To address specific points in the question:
Besides the above, additional parameters must be identified, such as:
Once these are nailed down, the selection becomes easier. These variables are the reason manufacturers like TI have such a vast selection of parts for fulfilling what is apparently the same purpose.
Further, this answer maybe of use to you.