Best type of Sub to consider?

Juan - Thanks, but the link you provided is not working.

Tom - Good information. I wasn't thinking so much about the hookup. One of the brands I am considering is sealed, and the cable it comes with connects directly to my Horning speaker posts. Then, I read on another brand's website that this is an inferior design flaw. So, another can-of-worms that can be opened up.

I have to think, that if I owned full-range speakers with forward firing built-in woofers, I'd be in good shape. However, many full-range speakers place their woofers in different locations, so on the sides and in the rear, like mine. These different designs must be designed around an ideal room layout. My Hornings want corners because they're rear ported, for example. This makes me want to believe that stand-alone subs are the same, so how they fire should make a difference to how the room is laid out.

In contemplating the right fit for my room, my best guess would be to use forward firing subs, and to try placing them almost up against the inside sides of my Horning speakers. If not a design flaw, it would then be easiest to connect the subs directly to the Hornings. However, in doing this post, I'm trying to extract the science of these different designs, so to take some of the guesswork out and reduce the number of subs to try.

As to adding subs in the first place, I have always been a purist and never cared for them. This is mostly from way back in the day when I could not find coherency in the combination. I realize, that I'm going to have to put out some serious coin to keep up with my Hornings. In these current times, I have been blown over after listening to the likes of the big Cessaro's, for example, with their add-on and powered subs. So, matching becomes critical, and I want to believe today, that a combination can improve my sound quality.

l have also heard, that there are audiophiles out there who are using subs with their Horning speakers. Are there any of you out there?
Kenny

One of the brands I am considering is sealed, and the cable it comes with connects directly to my Horning speaker posts. Then, I read on another brand’s website that this is an inferior design flaw. So, another can-of-worms that can be opened up.

In most cases connecting a sub that provides speaker-level inputs to the terminals on your speakers will work fine. The circumstances I can envision in which it would not be a good idea, and might result in hum, noise, or other issues, would be:

1)If the amp(s) driving the speakers have outputs that are balanced, meaning that both the negative and positive output terminals have signals on them.

2) If the amp(s) driving the speakers have outputs that are bridged, meaning that both the negative and positive output terminals have signals on them.

3)In a few cases, such as certain ARC balanced amplifier designs, where the amp’s circuit ground is connected to its 4 ohm output terminal, rather than to the "common" output terminal.

4)In the case of certain older class D amplifier designs, where both the + and - output terminals of the amp are offset from ground by a large DC voltage.

In all other cases, which comprise the majority of amp designs, I don’t think there would be any problem at all doing that.

Regards,
-- Al

Kenny: I'll share my thoughts, though I don't know your main speaker (which, I gather is a modified Lowther-type driver augmented with woofers and depends on corner reinforcement):
1. If I had to choose between a coherent speaker that was optimized for its full range vs adding on subwoofers to augment the bass, I'd probably do everything I could first to optimize rather than add. I know you said you have no options, but looking at that room, the side facing the system looks like it has "corners" (I assume there are windows behind the blinds, so you might have to deal w/ inserting some kind of rigid panel behind the "corner" blinds when listening). Perhaps with cabling, power outlets and the like, it's too much of a pain.
2. The notion of feeding the woofer amp from your main amp isn't crazy- my Avantgardes are set up that way and though their woofers are driven by their own internal solid state amp, the thinking is that they take on the behavior of the main amp feeding them (in my case, a SET amp).  The cables to do this made a difference- I went through various "jumpers" before I arrived at one that sounded better than the others.
3. The woofer design may be less important than placement and dialing in- read some of the other threads here- about swarm woofers, about dipole kits to match the behavior of panels. 
4. I've been messing with subwoofers for a long time for music and was never happy, having had various Quad loudspeakers (electrostats) and then horns. (I didn't even bother trying to sub-woofer my Avantgardes until quite recently). Right now, I am achieving some improvement using an unmatched pair of subs, crossed low, no roll off of the main woofers, and have been fiddling with DSP. I didn't want the discontinuity typically associated with subs and planars or horns, and didn't want to muddy the midrange. I've managed to get it 'just so'- more foundation without screwing up the mids---
5. Your system looks like it came from Jeff at High Water, who has very good ears, and is a cool guy. Even if he doesn't sell subs, does he have any advice for you?