I have a similar Onkyo AVR but it is an older model. Mine has 100 watts per channel @ 8 ohms. I have a pair of Thiel CS6 speakers which are difficult to drive (they dip to around 3 ohms) but are not especially worse than some newer speakers, particularly B&W or some of the Focal models. When I sent away my Krell KSA 300S for recapping I tried running my Thiels with the Onkyo. The difference was not subtle. I literally laughed out loud when I played the first song. The bass was anemic, the soundstage flattened, and it sounded sort of like an AM radio compared to the Krell.
My point is that an Onkyo AVR is not designed to run a speaker with a difficult load. If you go with a new set of speakers that you intend to run with your Onkyo I would pay particular attention to how they measure for impedance. Stereophile runs excellent impedance measurements in their speaker reviews. If you buy speakers with a difficult impedance curve I think you should seriously consider using a dedicated amp for the main speakers that can handle 4 ohm loads.
Regarding speakers, my only advice is that you seek out the new SVS Ultra Evolution Pinnacle and give them a listen. They are a little above your budget but I recommend you hear them to see what's possible for $5k. They are quite warm sounding with generous bass but they are very quick and detailed. They set a new standard in that price range.

