OK I haven't had time to read all of this thread properly, so apologies if this stuff has already been said.
For me,
Fire is absolutely the number one typing for this CAP. It brings lots of weaknesses and resistances, some risky moves (flare blitz, overheat, v-create, eruption, inferno), is strong offensively but resisted by large portion of OU and neutered by rain, and is weak to residual damage.
So having decided fire was best, I had a bit of a play with
this thing. To me it seems like
Fire/Ghost is completely ideal - in fact the only problem with it really is that we have Chandelure already, an excellent risky pokemon. It has a remarkable
4 types neutral to it, the lowest I could find without using Steel as a typing (Steel being crappy offensively). Not only that, but it offers up weakness to Pursuit and Sucker Punch, and a resistance to U-turn, which I actually think adds somewhat to the risk since it helps to prevent your opponent from playing safe themselves. Ghost is also a strong offensive type on the special side, but is rather lacking on the physical side due to a lack of good moves (this is the only reason really). It's definitely not spammable either.
Second to that I'd say
Fire/Psychic or
Fire/Dark as these also offer a good number of weaknesses and resistances, and a pursuit weakness in the case of the former. Dark allows the use of moves such as Sucker Punch and Pursuit.
@ Birkal mainly: I don't understand why immunities are bad. Are we not trying to exaggerate the effects of risk here? Switching in on a resistance is still "safe" if you know it's coming and your pokemon is healthy. However, if you have an immunity, you threaten to switch in at any point in the match merely by taking a risk. Immunities are better than resistances here. Neutralities, though, are the main problem, which is why I selected the typing I did. An imbalance in the numbers of weaknesses and resistances can be addressed through the use of defensive stats, but there's no good way to deal with neutralities.