lemans23;The amp you show in your link is intended to be mounted on the back of a sub box; it actually needs a hole in the back of the box to sit inside of; my KLH 10" sub has an amp with a similar design. For home use, it looks pretty good; as long as your not trying for high SPL.
The amp that berry47 shows is a pro, bridgable rack mounted unit that a band would use. It is a simple 2-channel amp that although it has gain controls, it does not have a crossover or phase selector. It was designed to run full range, not just subs. Its input jacks are 1/4" TRS or XLR plugs that use cables typically used by recording studios and bands for concerts. It is a strong amp though.
Which model type-S sub do you have? In any case, a single 4-ohm voice coil or a dual 2-ohm (Wired in series) would be ideal for the amp you've shown. If yours is a dual 4-ohm, then you will have no choice but to wire it in series for 8 ohms; but then your only going to get 150 watts out of that amp, which if I read Alpines' web site correctly, that's not quite enough to power the type-S sub diecently. The reason I say this, is the amp is only capable of going down to a 4-ohm impeadance load; not a 2-ohm.
How do you connect it to your reciever? From the sub out single RCA on the back of the reciever to the left RCA channel on the sub amp (Usually marked "mono"); if your reciever does not have a sub out jack, then the standard RCA stereo line out to the stereo line in on the amp will do. If that's not possible, then the amp you've got shown is eqiupped with a high power pass-thru; simply run the front left and right speaker wires to the high power inputs (Red and black banana jacks), then from the high power outputs, run wires to your front speakers.
Wiring it to your type-S sub? Like I said, this amp is intended to be mounted in a hole in the back of a box; most home-use subs use a ported, side-firing cube design. If your thinking of just running it not attached to any box, that may be possible too; but you will have to run wires into whatever sub enclosure you are using. The speaker wires attach to the sub and the amp just like a car amp; just remember what I said about the impeadance. There should be a pair of speaker terminals (Not shown in the picture) on the back-side of the amp.
Sorry if this was too long; let me know if you have any questions.
Later.