If the sources for the TV will be satellite only, then you don't necessarily need an HDMI processor/receiver. Satellite will always be compressed dolby digital, so you can go old-school. Even if you add on DVD/bluray, old-school digital COAX is still excellent.
The ELAC are excellent speakers for the money. They are passive speakers (require amplifier). The AudioEngine A5+ are powered speakers (amp built in). I don’t know anything about that product. However, if you are looking at powered speakers, I would recommend taking a look at the Emotiva AirMotive series. The AirMotive 5s are $499 (only 100 dollars more). They have better amplifiers (2x50 watts for each speaker instead of 1x50). The two internal amps power the woofer and tweeter individually. The tweeter is a ribbon driver, which will be cleaner and less bright/harsh than other tweeters. If you are interested, call Emotiva and ask if they have any “warehouse seconds”. These are typically items that are returned within 30 days by customers who are just “trying them out” – and they come with 1 year warranty. Even if they don’t, for $500 I don’t think you can buy better.
Then just look for a bargain basement HT processor, or a 2-channel preamp/DAC. An HT processor will provide you the ability to grow if you want to add a center channel or sub. Examples are B&K Ref 20 (if you want a warm sonic signature). Or Krell Showcase.
You can try to find a used 2-channel preamp with a built in DAC, but it’s likely to be much more expensive. Although I did look at Audio-GD. You can get an Audio-GD NFB-11.28 DAC/preamp for $330 plus shipping (probably about $50 to USA). The Audio-GD have been around for a long time and have always been very high sound quality. The ELAC + receiver combination is not going to be anywhere the level of sound quality that an Airmotive 5s + Audio-GD NFB-11.28 combination. The Emotiva/Audio-GD is going to be very high resolution and excellent. You would have to spend a lot more on a receiver to be able to match the Emotiva/Audio-GD level, and at that point you are going to be way over the $1,000 mark and it still may not even be as good (there’s just so much more you have to pay for in a receiver and it’s not worth the money if you’re not going to use it – such as 8-11 extra channels, room correction, HDMI, etc.). You should be able to configure your satellite receiver to output 2-channel stereo audio through the digital connection and then get a Blue Jean Cable Beldon 1694A 6 foot digital cable to connect them ($20). Another good thing about this combination is that both items will be new/newish and you will have good longevity (when compared to buying really old stuff).
Relating to my DAC recommendation. Just to let you know, I have spent the last several years, as a hobby, doing extensive R&D on DAC/preamp circuits. Modifying and rebuilding circuits, I/V, gain stages, power supplies. I have gone through many iterations to determine what works and what doesn’t (i.e. cap choice, negative feeback, I/V, power supply, op amp choice, etc. etc.). The Gustard X20 pro does many things “right”. Separate linear power supplies for digital and analog (where many others use switching power supply for digital sections – BAD). Metal walls to shield sections from EMI/RF. Excellent choice of caps and layout/design. Fully discrete analog output stage. Excellent digital clock (looks like a TXCO clock, maybe even an OXCO clock). Fully balanced/differential from the DAC chip. For $869, this DAC competes with others in the $2,000-3,000 level. You can read tons of forum feedback on this DAC. You will probably get a lot of other opinions for “best DAC”, but I think this is an excellent choice. I was actually planning on getting one of these next year for my next project because it is such an excellent platform/design, but I found a much better DAC to work with. I plan to get the LKS MH-DA004 which is twice as expensive at $1599 with USB (but it looks like a giant killer that will compete in the $3,000-5,000 area). Actually, the LKS is about 95% close as to how I would design something if I had the capability to do it from the ground-up. The Gustard is second at about 80% maybe.
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I took a quick look at the Yamaha 801. It’s pretty good. However, remember you are comparing a $799 retail integrated to a $2495 retail integrated. The Parasound is just going to be in another league. I do agree that the Yamaha would be a good choice if you are at that budget level. It looks like you can get a used one for around $475. The Parasound transformer and power supply look to be beefier. The Parasound is also going to use much higher quality internal components. The Parasound is just going to sound much more refined and could have a lot more brute force for bass punch/muscle.
As far as the Peachtree, I have listened to Class D stuff and I have decided that it is not for me. Many others love the Class D. When I listen, I can agree that it is extremely clean sounding. However, it just does not have that “organic” feel – there is no emotional connection for me to the music, also not as much high frequency “air”. Many others love the Class D, so I’m not attacking the technology. However, there are a couple companies that are putting a discrete Class A input stage on the amplifiers that make it sound sweeter and livelier. The two examples I know of are the PS Audio S300/M700 amps and the Nord “One Up” series (I would recommend the Sparkos opamp option over the Sonic Imagery if you are looking at one of these). I haven’t heard them, but I would think they would sound less “sterile” than the other Class D offerings.
If you are considering an external DAC like the Gustard, then there are probably better integrateds than the Parasound Halo. Especially if you are also looking at an external phono preamp. It really depends on your budget.
I do know someone who has excellent results with the PS Audio Nuwave phono preamp. Like I said, I have no experience with phono preamps, so I could not advise.
Speakers – this is difficult. If you post a question like “what is the best speaker for $1300”, you will get 15 different opinions and “everyone is right”, lol. And the recommendations will be all over the board, just making you more confused. Do you have a Best Buy / Magnolia Hi-Fi near you? It’s a good place to start. Just go in and ask to listen. It will at least give you an idea of basic B&W, Martin Logan, Definitive Technology sounds. Then you can post a question like “I like the sound of the B&W xx model speaker. Is there a better choice given the type of sound that the B&W provides”. Then you can get into a discussion on how one speaker is different from another speaker. Without a baseline, it’s almost like asking a blind man to describe what “seeing” is like.