I have not dealt in depth with Corolla audio (beyond installing H/U and replacing speakers), so I am not an expert.
However, I am in the industry, and have dealt with enough audio on other vehicles.
As a general rule, use good speakers up front and cheaper ones in teh rear (unless you can afford good speakers all around).
Most people (in north america) prefer to have more sound coming from in front of them (vs behind them), thus the good speakers (which you hear more) are in the front.
I will assume that you have a sub out (aka non-fader pre out), to which you are connecting the amp/subs.
Get a good amp. Also, you can never have "too much" power, but big power = big $$ & big size (space). For most "normal" people, 150w @ 4?/ch (rms) in MORE than enough.
If you get a good speaker but a cheap low powered amp, it can "blow" your "expensive" speaker.
Even if you hook up a cheap speaker to your awsome amp, you wont have issues dammaging the amp.
I am running a pair of 10" subs with an eclipse xa2000 in my truck. the amp sits under the driver seat
http://www.eclipse-web.com/amp/xa2000.html
I generally do not like booming bass (my baby is sitting the rear), but when I want it, its got power to spare.
For the most part, I like to have the little extra oomph of the kick drum when listening to music or the rumble when watching a dvd.
But if i want, the car will shake & buzz (i need to dynamat the vehicle)
In the saab, I will (project for next month) be running a single 10" sub with a 100w sony amp (dont rem what it was...)
I used this in my old saab and celica, and have enjoyed it enough to keep it every time i sold the cars.
again, more power than i need.
i think i have the gains up to 35-35% on the amps.
you mention audio pipe? no idea what that is, but is it powered? if so, yeah, you dont need any amps.
With all that said, like muzak asks, do you really need a sub? you could also go with a pair of 6x9 in the rear to give you the extra little bass.
it will save you a lot of trunk space and weight...
Finally, yes, Toyota offers a sub/amp package. However, as with any dealer, it will cost you an arm, both legs, and maybe some internal organs as well. For the price, you will get much more going with aftermarket.
so, for your set-up, my recomendation (i assume that $$ is an issue):
the pioneer speakers, are they in the rear?
1. get some decent front speakers
if you still want more bass,
2. get a decent 200-300watt 2ch amp & cheap sub (unless you can afford a "nice" sub). this should be more than enough power. or if you may want to just by-pass the amp on your current subs?
as for brands, there is no ONE brand that is the best. depends on your listening taste and budget.
good luck
tdk.