Hm. For the receiver vs amp, It depends on how efficient your phones are (measured in dB known as SPL (sound pressure level)). It's how much sound at a certain voltage your phones can create measured in dB. Also depends on their impedance, but that's secondary compared to efficiency for how to amp your phone.
An amp is to amplify the analog signal coming out of your source. Without it, you can't really hear anything unless there's that extra power (from the pre-out or something of the sort). Then at a gain of 0, you'll still be able to hear things since the signal is amplified, even if it's from the pre-out power. Don't take what I just said too seriously though, it's just what I can remember.
You'll also need an amp for the impedance of your phones. There's an output impedance (impedance of the output such as the receiver), and the impedance of your phones. You need your phones to be at least 8 times more to have less distortion/noise. You will possibly hear a hiss due to a high impedance output. For example, IEM/CIEMs have a lower impedance. Computer jacks and possibly iphone jacks (idk about iphone/idevice jack impedance) have a high impedance for the output. You put in the IEM/CIEM/low impedance phone and you will hear a hissing.
Then there's the simple get the amp for the extra juice that's needed to drive the phones or drive them to their potential. Amps also affect the sound, but not as much as changing your headphone (tube amps can take of a hot treble of w/e phone like a k702).
Now, as for surround sound phones. The phones here at head-fi that are known are dual channel/stereo, meaning the have 2 channels: left and right. The surround sound is more of a marketing ploy. People will use programs like Dolby Surround and mix-amps to play. I'm not sure how well games work with stereo though, but I'm pretty sure some phones w/ good sound-stage and position like the MDR-F1/MA900 would kick the butt of w/e "surround sound" phone there is.
Do you want open or closed? Is it for spatial placement or bass?
