why do most amplifiers, even the very expensive among them have mainly cinch connections? I mean shouldn't optical or HDMI supposed to be much better. I am really confused here.
Generally the more expensive and "exotic" the equipment is the more singular in function it becomes. The reason for this is that Audiophiles perpetuate the notion that this is more "pure" therefore it sounds better. While there is some truth to this it's not without its caveats. In order for an integrated amplifier or separate amplifiers and preamplifiers to achieve their tight specifications they would have to spend a considerable amount of effort and money to isolate each part of these components within the same chassis from one another to prevent interference. Without isolation you get excess noise.
A good example of where nearly no isolation is implemented would be in a all in one midi shelf system. I've seen these systems have a tape deck, DVD/CD player, AM/FM tuner, DTS & Dolby Digital decoders, MiniDisc recorder all in the same chassis and it's all poorly integrated. Basically the equivalent of assembling a computer out of spares, the performance leaves much to be desired.
Home theater receivers benefit greatly from market saturation. Because they sell a given model in such a quantity they can afford to engineer and manufacture reasonably priced home theater receivers that perform quite well. Next to their integrated amplifier brethren they cost less and offer more and frequently they offer better performance for the same money even from the same manufacturer.
Integrated amplifiers are typically easier to operate, because they are minimalist and sparse. They don't sell near the same quantity of these as they do the receivers.
HOWEVER! You being in the UK makes that performance gap per dollar a whole lot smaller because Europeans are far more likely to buy integrated amplifiers. But the better value is still probably going to be found in home theater receivers.
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I'm having trouble finding information about your speakers. I cannot find the impedance. I suspect they are likely to be 4 ohm nominal and may dip lower to achieve their advertised frequency response (referring to the towers). If they are as power hungry as they appear they might be, the TX-NR636 may prove to be unsubstantial. You might need to look at NAD, Arcam, and higher models from Onkyo, Yamaha, Denon, & Marantz. You might find you may need to go a little over budget to get what's necessary to drive them.
EDIT: I found this.
Chrono SL590DC:
• Standlautsprecher
• 3-Wege-System
• 160 Watt Dauerbelastbarkeit, 320 Watt Musikbelastbarkeit
• Frequenzgang 47 Hz – 38 kHz bei -/+ 6 dB, 52 Hz – 24,4 kHz bei -/+ 3 dB
• Empfindlichkeit 88,3 dB
• Abmessungen (BreitexHöhexTiefe in cm) 19 x 105 x 30
• Nominalimpedanz: 4 bis 8 Ohm
• Gewicht pro Stück 21 kg
For some reason it was advertised as 20Hz-40kHz, these specifications are far more meaningful. You may be able to squeak by with the Onkyo.