But it sounds like if I have HDMI connection everything should work, right?
Correct. Even old 480i will pass work.
Budget is roughly under $1000. The Marantz has gotten good reviews, it's on my short list already. I was also looking at the Onkyo NR636, the Sony DN1050, and the Yamaha line(s). According to reviews, the Sony (surprisingly) has better sound than the Onkyo, and the Marantz has better sound than the Sony. But I haven't found any comparison between the Yamahas and any of the others. I'll check out the HK - had an HK amp many years ago and thought it had great sound. Anthem is tempting but a good bit more expensive. Any opinions on whether it would be worth the extra bucks?
Well Anthem looks right, nice and spiffy, and it really sounds good, but I'm not familiar with their customer service and support, nor about their durability. I like the Anthem MRX-510's rear end and specs, but it is an expensive piece of kit.
I'd stay away from Sony as a matter of principle. I'm not comfortable with Sony stuff since the Rootkit-Gate. And to add yet another point against it, it has no multi-channel analog, even though Sony have been big promoters of SACD and DVD-A in the past, both formats require multi-channel inputs, and one day, they build receivers like SACD and DVD-A never existed; no respect for anything, these guys...
Yamahas are nice, but can't say I've auditioned one in the same price range. I've heard the AVENTAGE CX-A5000, it is an impressive beast, but the price is just... Intimidating.
A note on HKs... I would pass on newer HKs. This was a suggestion for the older models from used market, if budget is really tight.
Newer models , I would avoid. Mr. Harman passed away, and the new head cheese has already toyed with commitment to quality sound. Newer models have an overly simplified and dumbed-down connectivity group. The new class D amplifier unproven, and are often vilified and reported to be made with questionable parts. I don't know much about the class D thing, but I don't trust it, and don't trust the new Harman management. I think the two models mentioned above are quite OK, but they where the last "worth their salt" coming out of HK.
A newer model with multi-channel Analog and perhaps a phono pre-amp could win me back to HK, but It could only happens if they brought back their traditional power supply.