Right now the beast family has my favourite pets. But it is starting to get a bit silly, dangerous and stupid when I more and more got with three beasts. One mech and I am screwed.

I will focus mainly on PvP aspect, can't really say that I have any general PvE beast pet.
Mr. Grubbs and the other beast Maggots are very tough guys. I rarely use them though, but I do have a spot for them in PvE. There is one player on my meta that uses maggots and I always find it fun when I run into him/her. It's a hard nut to crack.
Xu-Fu can be a real pain. But the problem with any Prowl pet is that the move is telegraphed in advance and if your opponent has any kind of avoid/stun you just wasted a lot of turns. That said I truly love to stun a prowling Xu-Fu. But without avoid/stun Xu-Fu is a tough customer.
S/S breed Death Adder Hatchling is probably one of the most powerful beast pets available, but it has lowish health and does have some counters. The main problem is that a fast blinding poison is a very powerful move in PvP and have many uses.
My own favourite beast family pets are:
1. Vengeful Porcupette. This beast is immensely useful in the current environment. It has strong attacks vs undead and it is a good counter against Death Adders and Flying pets. It does have some really tough counters, but I find this one does really well against most pets.
2. P/P Baby Ape. This powerful pet hit insanely hard. It can solo a non-demolishing Anubisath Idol and a Crawdad on it's own. It just hits that hard. It also comes with a useful stun(hi Xu-Fu). There are some Apes that are faster which will get more use out of the stun but 325 power of the Baby Ape just hits that much harder.
3. H/H Elder Python. Also another hit that can hit insanely hard. It does have some issues with hit rate. But it has poison which is strong vs mechancials, a stacking attack that ramps up really quickly and a hit-hard 2-turn slow which is very handy.
A couple of more I really like.
325 power Worg. With Flurry, Crouch and Dazzling Dance it can take out any undead really quick and has no trouble handling Decoys of Mechanical Pandaren Dragonling.
P/S Arctic Fox Kit. Similar to the powerful Worg. But the 289 speed and Dazzling Dance means it will be faster than Death Adder Hatchlings and can handle them pretty well.
Kovok. I run it with Poison Fang, Digest Brains, Black Claw. Black Claw will pretty much nullify any Sandstorm/Shell and is not only useful on the Kovok itself. I also love how the Kovok can handle any Sunflower/Blossoming Ancient/Crawdad, and come out on top.