With capacitors, there are four things to pay attention to:
1) Capacitance typically measured in microfarads (uF).
2) Voltage, measured in V.
3) Polarity, usually indicated by a stripe or marking on one of side of the capacitor
4) Package size (height, width, and lead spacing)
Capacitance
For capacitance most of the time you'll want a capacitor with the identical capacitance. In the first and third picture, those caps are 330uF. So you'll want a capacitor that is also 330 uF. The second picture is 1000 uF.
For surface mount caps, markings can vary, but typically the large numbers will indicate the capacitance. In your case it looks like you've got a couple 1500uF caps, 1000 uF, 470uF (green), and 82uF (purple).
Voltage
For voltage, you'll want a capacitor with either the same or higher voltage. The top caps all look like they are 6.3V. You'll want two 330 uF capacitors with 6.3V or greater and one 1000 uF with 6.3V or greater. For the surface mount caps, most of them are 6V expect for the purple which is 16V.
Polarity
For polarity, if the capacitor has a stripe running down one side, that indicators the negative side of the cap. You'll want to replace the capacitor with one that matches the polarity, so pay attention to which side negative end is soldered to on the board.
For the surface mount caps, the polarity is indicated by those black/colored shades on the top. The side with the shaded part is negative.
Some capacitors are non-polarized and won't have this particular stripe. Not sure if this is the case for the first three caps without seeing the other side of them.
Size
Finally, there is the physical size of the capacitors. The most important is usually lead spacing. It's not 100% critical (since leads can be bent), but it does make for a neater install. Physical width and height can also be an issue sometimes, depending on the space on the board or enclosure.
My general rule of thumb is to obtain caps with identical specs as the originals. I typically use Panasonic or Rubycon branded capacitors as they tend to be high quality. Mouser and Digikey are good places to order from.
One last note: I would skip replacing the surface mount caps unless necessary. Removing and replacing surface mount caps can be a bit trickier and you can more easily damage pads if you're not careful. If you haven't worked with surface mount items, I'd recommend practicing on a practice kit or sacrificial board first.
