The filters (cross-over) on an amp will be better than on the HU. The Arc 4080 looks like a great amp.

If you run a passive set-up, turn off the filter on the amp and let the component cross-overs do the work.

If you run an active set-up, you'll need to set the filter slope and filter freq.

My set-up:
HU - Alpine 9887 w/ HD tuner
Comp - DLS Nordica 6.2
Amp - JL Audio HD4/600
Wire - KnuKonceptz (speaker, power & RCA)
Sound Deadener - eDead V3 & eDead80
No sub yet
Condition of car - Total train wreck! lol In the final stages of my build. Will be glad to get the interior out of the tub.

JL, Kicker, Rockford Fosgate and Boston Acoustics have good subs at attractive prices. JL & Rockford always get good reviews from what I've found. Most local audio stores will carry a good selection of subs you can audition. I'll let other members chime in with their preferences as I've never been much of a sub guy.

 

The JL Audio 10W6 might be out of the question if I choose to use one of the ebay MDF enclosures that are recessed. I want recessed so I don't squish the sub with gear.

Looks like max height is 6" for the recessed trunk enclosure (2nd ebay link) and it is .75 cubic feet in volume.