A sealed box is easier to build, the only tuning is the final net internal volume; my first subs have been sealed to make it easier on my beginner woodworking skills. Bigger boxes will need some internal bracing, so a bit more than a basic box but not by much. Vented/ported subs will take some calculation/modeling for a given port tuning, but the nice thing about these proven designs like I linked is that's already been done for you. Here's
another series of sub with much of the legwork already done for you.
You should have dsp to set a high pass filter to protect the driver if you go ported/vented; for a sealed sub dsp is nice to pull the bottom up a bit due to natural roll off of a sealed design.
You don't need a separate crossover unit if your avr can handle that part but a miniDSP can handle both the dsp/crossover duties if needed or a Behringer iNuke DSP series amp if you want it combined with the amp (there are other amps with such, but Behringer is pretty popular for a low cost solution).
I use Crown XLS amps with my sealed subs, and even just Audyssey will do a decent job of eq'g them (but I have a minidsp for setup as well). Crown and Behringer are popular amp choices in any case. I'd read thru the DIY sections here and at AVS and diyaudio.com for some background/guidance.
IMO subs don't care if its music or HT, accurate reproduction is accurate reproduction....