Recently, I had the opportunity to use my KEFs with two different amps: A Sony STR-SE501 AV receiver and a Bryston B100-SST integrated amp.
To be fair, I picked up the Sony at a thrift store for an inexpensive audio system in a spare room. The Sony is rated at 100W into 8 ohms and is 4 ohm capable with a slide switch. Its spec is THD 0.09% and SNR -96 db at a reference level that is unknown to me at this time. The Sony was able to drive the KEFs to my listening level (60-75 db) with no issues - I didn't try to push it, as it was merely being used as a back-up. The sound was a little bright, but pleasant. Bass was all there. There was some low-level hiss/noise that was masked at higher volumes. It sounded a bit flat and 2-dimensional, but okay for background usage. I was not wowed, but I was not repelled, either. The point here is that the nominal 100W mass-market amp had no glaring issues with the load at reasonable volumes.
The Bryston, on the other hand, was spectacular. Very clean, very neutral, very detailed. Much less background hiss/noise. The Bryston is rated at 100W int 8 ohms and 180W into 4 ohms. The sound quality rivaled that of my main system with more expensive Thiel & Bryston components (with less bass, of course). I'd highly recommend the B100 or B135 if it's within your budget - it plays superbly with the LS50 and really shows what the speakers are capable of.
So, my finding was that 100W of rated power is more than enough for this speaker pair if the amp is 4 ohm compatible.
However, the higher quality the amplification, the better results you will get from the LS50. It responds well to quality (high SINAD, flat FR, high dynamic range, etc). Feel free to start with a mid-range amp and move up as your budget allows if you like the sound from this speaker. What is upstream of the LS50 is likely to be more of a restriction than the LS50 itself.
My NAD is currently being refurbished at Quirk Audio, hence the "pinch hitters".