Here are some ideas. I hope that these team suggestions can inspire you to make your own combos.
1. Anubisath Idol (Crush, Sandstorm, Deflection), Blighthawk (Infected Bite, Ghostly Bite, Lift-Off) , Strand Crawler (Snap, Healing Wave, Shell Shield)
The idea behind this team is quite simple. You combine three stand alone pets that are strong individually. This team provides some type coverage. To give a few examples of type coverage. Enemy undead attacks; Anubisath Idol is weak, Strand Crawler is strong. Enemy critter attacks; Blighthawk is weak, Anubisath is strong. Blighthawk provides damage and avoidance. Anubisath idol has avoidance and a strong defense. The Strand Crawler has a strong defense and it will be good against all the Unborn Val'Kyr and Death Adder Hatchlings that you will encounter.
Note: Always start with Shell Shield versus Death Adder Hatchling and other pets with multi-attacks/dots.
Surge can work well when you do not like Snap. Snap however is easier to use.
Pros: This team is an easy to use team and it has a lot of potential.
2. Anubisath Idol (Crush, Sandstorm, Deflection), Blighthawk (Infected Bite, Ghostly Bite, Lift-Off) , Leopard Tree Frog 325 speed (Tongue Lash, Healing Wave, Frog Kiss)
This team works the same as the previous one, although I find it more interesting. It uses three strong stand alone pets, although the Leopard tree Frog is arguably worse than the Strand Crawler. It however provides better type coverage. I like using a pet with high speed and I like having a variety of moves.
The Leopard Tree Frog counters any undead. This team would probably perform worse than the one with the Strand Crawler. Sandstorm can reduce the damage of your frog if you mess it up, which you most likely will at some point or another! Strand Crawler counters more common opponents . I however dislike having a shield x2 (Shell Shield+Sandstorm) on one team for no good reason.
3. Nexus Whelpling (Frost Breath, Mana Surge, Arcane Storms), Blighthawk (Infected Bite, Ghostly Bite, Lift-Off), Ghostly Skull (Shadow Slash, Ghostly Bite, Unholy Ascension)
This is a gimmicky team that works with the weather effect Arcane Storms. Mana Surge does additional Damage, Ghostly Bite does not recoil with a stun. You start with Nexus Whelpling with Arcane Storms and Mana Surge when it is favorable. After that you set up the Gjostly Skull with auto-attack and Ghostly Bite whenever you can. The same goes for the Blighthawk, although this pet has avoidance and can hurt aquatics through Lift-Off.
This team is gimmicky and not very strong. It can easily be countered. However, when you are not countered your damage output can be very high. This will win you matches.
Note: You can swap out Infected Bite for Slicing Wind.
4. Darkmoon Tonk (Missile, Minefield, Ion Cannon), Snarly (Rip, Surge, Blood in the Water), Electrified Razortooth (Rip, Blood in the Water, Lightning Shield)
The idea behind this team is quite gimmicky, but it can do well. The idea is to do heavy burst damage. The combination of rip with blood in the water is amazing burst wise. Minefield can protect you from having an opponent who swaps out of being 100% hit by Blood of the Water, although double rip can be quite good.
This team has some minimal type coverage.
Cons: Your winratio will improve drastically with experience/knowing favorable match-ups. This team promotes swapping.
5. Darkmoon Tonk (Missile, Minefield, Ion Cannon), Snarly (Rip, Surge, Blood in the Water), Kun-lai Runt (Takedown, Frost Shock, Deep Freeze)
This team works similar to the other team with Darkmoon Tonk and Snarly. You however replace one pet that benefits from swap-protection with another pet that benefits from swap-protection. Frost Shock followed by Deep Freeze will give you additional damage from Takedown, while their pet is stunned. It has slightly different type coverage.
6. Strand Crawler (Surge, Healing Wave, Shell Shield), Pandaren Water Spirit (Water Jet, Healing Wave, Geyser), Lil' Bad Wolf (Claw, Dodge, Howl)
This is again a gimmicky team. It is build around getting an advantage through one combo. This combo is: You use Geyser then you swap to Lil Bad Wolf. Then you dodge (if you are faster, else Claw) and Howl. You will now have almost killed a pet through double Geyser damage. Claw can finish this. This will generally give you an advantage if the enemy does not have avoidance. Strand Crawler will provide type coverage, coverage for pets that are faster than the Lil bad Wolf and it can sweep swapped out pets with surge in the end-game.
Cons: Avoidance completely counters the strategy of Howl+geyser.
7. Clockwork Gnome (Metal Fist, Blitz, Turrets), Voodoo Figurine (Shadow Slash, Wild Magic, Sear Magic), Scourged Whelpling (Shadow Flame, Death and Decay, Plagued Blood)
This is a team made around the Clockwork Gnome with its Turrets. Turrets will hit multiple times in a row for quite a few rounds. This can create synergy with the other two pets. You can increase the damage of Turrets substantially through Wild magic, or you can recover and heal through Plagued Blood.
Note: You can use Call Darkness instead of Death & Decay. They both have different advantages.
Cons: This team promotes swapping. Shields can be difficult to play around. You might make many Sear Magic mistakes when you are starting out.
I have used teams 3,4,5,7. I have used team 1,2,6 using the same key abilities/concepts using slightly different pets. I have fought against team 1,2 minus the Blighthawk. I could recommend all these teams, although I had the better winratio with teams 4,5,7. I however expect team 1,2,3,6 to perform better for you.