A good flier is also helpful for clearing out backline additions if you are hunting anywhere in Pandaria, as aquatics abound.
Emperor/Spire crabs are pretty useful in that they are very durable during the catch phase (shell shield + heals) and can quickly eliminate backline adds with their Snap (strong vs critters). Crabs are also rather easy to acquire at a relatively high level (*tip-make sure to switch to Surge, rather than Snap, if attempting to catch a critter with a crab).
Any capture team is essentially nothing more complicated than the following:
1st pet - Self-healing tank that is not weak to the pet being captured (i.e.- Don't use a humanoid tank to catch undead, etc.)
2nd pet - High DPS to clear out most common backline type (i.e.- Beast if most common backline is critters)
3rd pet - High DPS to clear out second most common type of backline pet.
The only real change is switching in a Turnip or Corgi if there is any danger of accidentally killing the pet you are seeking (highly recommended on anything <L10ish or excessively rare).
Tanker- Crabs, Sporeling Sprout, Emerald Whelpling/Protodrake, etc. (any pet with defensive shield +healing)
DPS- Kunlai Runt, Flayer Youngling, Feline Familiar, any Timeless isle moth or WoD wasp, etc. (I prefer strong DPS with a self-heal so I only have to return to a stable master for renewals extremely rarely).
Some pets like the Turkeys or Lil Leftovers (with Food Coma) will actually put a pet to seep for several rounds while you try to capture them (be aware this tactic is ineffective vs critters whose racial grants them immunity).
You can easily find alternative pets to use using the "smart pet search" feature of the main page here. Type in the the family you want to use, then select "healing" as the modifier & it will find pets of that family type that can heal (pretty much everything except the Elekk Plushie has damage options). Alternatively, you could just use a healing pet to top off your capture team after every few battles, whatever you prefer.
Another tip- a select few wild pets like to kill themselves rather than be captured. If this is due to a specific ability (and not backlash damage from an attack like Body Slam), when you start the battle, check the ability lineup of the desired capture. If it has the self-kill ability on it's ability bar, you can flee the battle (as long as you have not killed a pet). You may do this as many times as necessary until the capture target does not spawn with the self-killing ability. This is especially useful on super-rares like the Unborn Valkyr, since you rarely see them and they are heavily contested.