Out of curiosity, is there a particular reason you're looking at only Onkyo and Pioneer? I hate to rain on an OP's parade, but I'm going to do that just a little bit...
I'd definitely want to talk with recent owners of Onkyo gear before I moved on one. While they were still excellent 15-20 years ago, I've heard loads of horror stories right here regarding HDMI problems related to the board, running obscenely hot and poor customer support. I believe they've improved in the past few years, but you can only go up from the bottom, right? Anyway, do a search in the forums for Onkyo, you'll probably find plenty if somebody doesn't chime in here shortly.
I've always liked Pioneer and owned a couple of their receivers. But one thing I've noticed about most of these brands is that they go through cycles of quality and innovation - and just caring. Pioneer sort of dropped the ball on Elite for a while, and let the rest of the world pass them by. I think they're in catch up mode. You'll probably notice a lot of the Pioneer Elite is on closeout or not available (I have), which hopefully means they're getting their act together with a new generation.
Yamaha builds some pretty solid (if slightly pricey) gear, and at the moment seem to be scratching their way back to the top again. I've owned a lot of Yammy, and no doubt will look to them for other products (particularly the CD-S2100).
At the moment, I'm starting to shop to put together a home theater system from scratch. But I'm going to settle on the front end before anything else. The budget brands I've narrowed down to are Yamaha, and sister brands Marantz/Denon (D+M Group). The latter 2 might slightly outdo Yamaha but it's a photo finish.
Things to consider are room correction, streaming (and what services are supported), multi-zone audio (other rooms a possibility?) and a decent DAC. Also important if you don't have speakers is if the unit is rated to 4ohms. With your Klipsch, it's not a concern.
What I'm looking at has more bells and whistles than I'll need, but I don't want to wish I had something that's not available. Other brands I've looked at and worthy of consideration are NAD, Outlaw and Anthem. If you think you're going to stick with a single system for a while, then I'd definitely be looking at these as well.
I'd recommend reading as much on the products you are considering as well as YT reviews. Not that any reviewer has better ears than you do, but often they'll bring up points they discover using the product. Things like you can't do "X" with the receiver, only "Y". And, it's something you might not have thought about. I also go to the manufacturer website and download the manuals. I can learn more doing that than a dozen reviews.
Right now you can pick up a Denon AVR X3600H or X4500H for $1k. I think those are overkill for your needs, so you could cut that in half with an X2600. Klipsch are exceptionally efficient, so you don't need oodles of power or current to get the best out of them. Good luck on your hunt - but take your time as this is probably the most important decision of all. A good receiver will give you everything you need to get started listening to music immediately.
