If your output voltages are fixed you should be able to design it with linear regulators with a minimum of voltage drop over the regulators. And 1A is not the end of the world.
A switcher would be more appropriate if you have a variable output voltage. A linear regulator which can supply 30V @ 5A, but which is set to 1V out it will have to dissipate 150W.
An SMPS is dimensioned for a certain input voltage, output voltage and current. If you would vary the output voltage its efficiency will be lower. You won't get the 90% figure manufacturers boast about over you full range, maybe more like 75 to 80%.
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If you want the +/-15V adjustable I'd go for the SMPS, for the dissipation reason I mentioned. You can attack the ripple with a pi-filter. A high frequency switcher (like 1.5MHz) will allow for a smaller coil.
If you want to test capacitors fully, you will need what is called an ESR meter(Equivalent series resistance)
Electrolytics have an ESR which increases through general use (age and heat are main factors).
SMPS (Switch-mode power supplies) are pretty sensitive to ESR. The ripple voltage on the output is calculated as \$V_{ripple} = I\times ESR\$. This means that as the ESR of your caps increases so does the amount of voltage ripple. I can't say with certainty the problems cause by ripple voltage so I've included an extract from Wikipedia.
Effects of ripple
1. Ripple is undesirable in many electronic applications for a variety of reasons:
The ripple frequency and its harmonics are within the audio band and will therefore be audible on equipment such as radio receivers, equipment for playing recordings and professional studio equipment.
2. The ripple frequency is within television video bandwidth. Analogue TV receivers will exhibit a pattern of moving wavy lines if too much ripple is present.
3. The presence of ripple can reduce the resolution of electronic test and measurement instruments. On an oscilloscope it will manifest itself as a visible pattern on screen.
4. Within digital circuits, it reduces the threshold, as does any form of supply rail noise, at which logic circuits give incorrect outputs and data is corrupted.
5. High-amplitude ripple currents shorten the life of electrolytic capacitors.
Now to answer your actual question. As long as the capacitance and voltage rating match that of your current capacitors then that's all you need. Personally I'd recommend Panasonic capacitors, every time I change an aluminium electrolytic I always change it for a Panasonic capacitor.
The backlight of your monitor shouldn't make any difference to the capacitors you need on your power supply.
Best Answer
stevenh already said it pretty good, but most likely they are decoupling capacitors.
Decoupling capacitors, or bypass capacitors, are capacitors meant to smooth power flow into specific parts of the circuit or into specific ICs. Changing power demands will create a "sag" on the power supply as it changes to meet output current demands. This pulls down the voltage. These capacitors will act as "local storage" to the load during a transient event that effectively masks the sag on the power supply to the load being bypassed/decoupled.
In a very dumb downed way, think of it like a pipe. One end is your power supply, and the other end is your load. The power supply adjusts itself to supply what the load is demanding. If the load changes, it might temporarily take enough water (power) out of the pipe to the point where the pipe isn't entirely full. The pipe not being full is the equivalent of your voltage sagging. This is what happens all the time on a power supply... load changes, and the voltage sags slightly as the power supply tries to supply enough current to meet demands... then eventually the voltage comes back up once the power supply has changed its output current to meet demands.
Now, a decoupling capacitor is like adding a big tank on top of the pipe. When the pipe is full... the capacitor can't empty any of its water out. However, when the load gets big enough and the power supply can't supply it quick enough... the tank lets some of its water out to keep the pipe full until the power supply can supply the given current.
As far as why they are different values, different parts of the circuit will require different amounts of power. Usually you'll see big caps (in the tens of microfarads, in this case, those big 100uF ones) near the power supply output itself... I usually see this referred to as "bulk"... this is for really big transients that pull a lot of power. Smaller values are for things with smaller current draws.
There's also some math behind the capacitance, I believe, in regards to how fast the capacitor can give up its energy for a transient event. Smaller capacitance being better for high-frequency transients, etc.