Running Bronze Triad setup with Onkyo TX-SR508

You won't be able to add an amp to that receiver. The receiver needs to have pre-outs to utilize an amp.

Think you will be ok without amp.

According to your desired needs, 80 "receiver" watts per channel will not likely be sufficient to really do what you want. 80wpc in an AVR will really be 1/2 that or less with all channels operating. I would go much higher if you want to stay out of clipping and have music that sounds high quality.

Onkyo usually delivers on their power claims (or fairly close; the 608 gets within a few %, and we don't care about a few % - even 50% is more or less inconsequential (3 dB is nothing to write home about)). Even if we're only talking about 50wpc ACD (ACD not mattering to anyone but marketers and salesmen) it's still more than most any domestic setting is likely to need, and there will be no "sound quality" gains by having a more powerful amplifier giving you the same 500-2000mW nominal that you'll want during normal listening; you just spend more money for capacity and feel-good that you don't benefit from.

The speakers you've picked are rated at 90 dB/W which is sensitive enough that even if the Onkyo delivers 50wpc (which we don't care about) it will get very loud very easily. HOWEVER, they are also 4 ohms nominal, which I'm fairly sure the 508 manual will advise you against (it specs 6-16), especially for high output levels. I'd probably pick a different set of speakers; a fancier receiver will cost more, and an outboard amplifier will cost a lot more. If you must use these speakers, you can throw an amplifier onto that Onkyo through a transformer (there are some multi-channel DIs that will do this too), but it may not be cost effective to do five channels like this.

You don't need 200W - unless you're meaning that's the specs on the speakers.

The $500 price point is the problem - there's plenty of receivers that can handle 4 ohm loads and remain stable, but at $500 that's asking to move mountains. The 609 and 709 are probably where I'd start, but I'd very honestly suggest nudging the budget up a bit, and looking at something like the 4311 or something in it's league. My experience is that Onkyo's run hot normally - having them drive a mess of low Z speakers probably won't help them.

Alternately, get the Onkyo, and grab an outboard amplifier - the XPA-5 is a great choice.

Pre/pro will cost more. No benefit unless it has some I/O feature you need.

I'd really just look at stepping the budget up slightly to around $1k, and picking a more competent receiver. The 1009 for example, or the 4311, or something like that.