So I'll admit this is closer to a team than a core, but seeing as how there are just so many options for additional teammates and since the metagame is still in its infancy therefore I'm having to predict threats from last gen/obvious threats from this gen (Greninja, Aegislash) I've got a core four I feel really good going forward with
Mega Charizard Y @Charizardite Y
Naïve Nature
252SPA/252 SPEED/6ATT
Fire Blast
Solar Beam
Focus Blast
Flamecharge
YZard suffers badly from 4MSS, so its very important to decide what threats you will be build around and which threats you want him to take care off. I decided that Dragons would be the type I'd trade off for a speed boosting move (Flamecharge) and I'd risk Focus Miss to hit Heatran and Tyranitar.
Venusaur @ Life Orb
Chlorophyll
252SPA/252SPEED/6SPD
Leaf Storm
Growth
Sludge Bomb
Sleep Powder
Covers YZards weakness' well, being able to remove Water and Rock types as well as being resistant to Electric. The idea is simple. Saur can either revenge kill w.e knocked out YZard, or hit TTar or the other weather inducers hard with LO Leaf Storm. Ideally he'd have a turn or two of Drought leftover to ensure either a +2 Growth or at least to outspeed w.e. comes in. If something Saur struggles with comes in, try to predict it with Sleep Powder and bring someone else in.
Snorlax @ Choice Band
Thick Fat
252ATT/252SPD/6HP
Earthquake
Pursuit
Return
Wild Charge/Thunder Punch
With Thick Fat, he resist two things that Saur is weak to, Fire and Ice. The EV spread ensures he can tank some heavy special attacks from Psychic types that also hurt Saur and then Pursuit trap them. EQ is there as coverage for Heatran if YZards Focus Miss doesn't do the trick, and just to generally remove opposing Fires. Wild Charge is just to round out coverage for Water and Flying types, although this is more of a last resort type of move since I can't get the Psuedo STAB Fire Punch until Pokebank (Note, Thunderpunch is also an option that can be added after pokebank).
Klefki
Leftovers
Prankster
252HP/252SPD/6DEF
0ATT IV's
Thunder Wave
Substitute
Swagger/Draining Kiss
Foul Play
By far, my favorite monster of Gen 6. This guy is as hilarious as he is effective. I slashed the Swag set, partly because as fun as SwagKi is, it's entirely luck based, and Draining Kiss, while weak, does recover good bits of health when it SE hits Dragons. This guy is mostly here for said Dragons, as well as to help slow down potential sweeps. Until I'm entirely positive who else will round out the team, I will continue to alternate between SwagKi and StallKi.
I've mostly battled over WiFi and not on Showdown so the core isn't tested against quality opponents, but I'm fairly confident in this core as long as I round out the remaining weakness'.
Moving onto said weakness', the PinkBlobs and Special Walls will give this core some trouble, as well as entry hazards. For spinners, I've had a tough time deciding between Donphan, Starmie, or Tentacruel. Out of the three, Phan is in the lead due to being able to hit Ghost types with Assurance, resisting Rock, and additional EQ support which is always nice, although with the weather nerf, his weakness to Water is highlighted since Drought won't keep that at bay. As for the other entry remove option, Defog, I don't have any idea who would be a good teammate for this core that has access to that move, so input on that end would be appreciated.
For physical attackers, I'm pretty much in the same boat of lack of ideas. Conkeldurr seems like a solid choice, but he really only serves to remove the two blobs and doesn't add much from there. Any ideas on that end would also be appreciated.