Is your tele routed for a p90?
Soapbar and dogear are essentially 2 different mounting systems. The pictures show soapbar p90s, dogear ones have little triangles on each side for mounting.
If you want the pickups to be hum cancelling in the middle position, one of them should be RW/RP.
May as well go for braided unless you want to do wiring mods like series/phase stuff.
I wouldn't use a P-90 for Hardcore ever, it would work fine for pop Punk.
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I think it will work pretty well for what you want.

Maybe also get a noise gate.
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usually the neck pickup is RW/RP, so get a regular one.

from the site:
2 conductor + screen provides the start and finish of the coil and a separate ground making it easier for series or parallel connections with more than one coil while braided 2 conductor has a single internal conductor and the braided jacket is effectively the other conductor and used as ground.

you only really need 2 conductor + screen if you're doing funky wiring, which I assume you're not doing, so just get the braided 2.
By funky wiring I meant any extra switches for mods, etc. I'm assuming your tele just has a 3 way and 2 knobs.
Dogear pickups have little triangle tabs on the ends of them which mount the pickup to the body. They're usually used for Les Paul Junior and SG Junior style guitars and for archtop (ES/Dot) guitars. Almost every other kind of guitar uses soapbar P-90s.
Also, soapbars come in two slightly different sizes, one specific to Gibson and one which fits most other brands' routes. Make sure you get the right cover and base for your guitar.

As for polarity and such, that depends on what the other pickups in the guitar are. In the case of P90s, having one pickup being RW/RP means the two pickups will give you a hum-cancelling sound when both pickups are used together (note: this does not sound like a humbucker pickup, it's just hum-cancelling). If both pickups are the 'stock' polarity, you'll still get hum in the combined pickup position.

2 conductor + screen wire is only used if you're going to use a coil tap, or some odd phase switching. Since it doesn't sound like you'll be using those, don't worry about it.

Personally, if I were looking for a P-90 to play pop punk and hardcore, I wouldn't use the Supermassive. I'd get a stacked design, like those that Gibson and Seymour Duncan sell. That way you get a hot P-90 tone but you won't have any annoying hum no matter how high you pump the gain (which a noise gate doesn't combat effectively, at least not without ****ing with your dynamics).
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