Help selecting integrated amp for ls50


Hey everyone,
its been a long time since I e posted here but it's time to upgrade my system and I need suggestions. 

Im thinking heavily of picking up the ls50s (although I've selected these without auditioning them since no shop here has demos).  I needed something small and in a white color (and yes, these factors were influenced by decor and my wife).  So if I do choose the ls50s I would also need a integrated amplifier.  I've read tons about the necessity of careful matching of room, amp and placement so I thought I'd better ask here before I pull the trigger. 

The room ithe system will be in is concrete and is about 15'x23'. It's a combined kitchen and living room no separation. There is carpeting on the living room which is 15'x13'. The speakers will be on a sliding shelf from a wall unit/ cabinet system. The shelf will allow the speaker to stick out of the cabinet. 

Budget is ideally <$1,000 for the amp but I'll likely get a used one to maximize the buck. Any help would be really appreciated!



autre
Post removed 
Putting the vibration control is a great suggestion. I'll look into that. Any other amp suggestions?
@autre~ I have used the Naim Nait 5i italic, Unison Research Unico and currently a SimAudio i3.3 DPX integrated with the LS50’s.

regarding speaker isolation I can highly recommend https://www.amazon.com/IsoAcoustics-ISO-L8R155-Medium-Acoustic-Isolation/dp/B008GOP79G/ref=pd_sim_26... Isoacoustics makes several models that work very well with monitor/bookshelf speakers.
Hey Tom5987, how would you rank the three you've used?  Thanks for pointing me towards some feet, that was one of the tjhings I was going to ask next
To be honest all three have worked very well. Musical, dynamic and well balanced. I guess that I would prefer the SimAudio because it is so versatile. My unit has the DAC, PHONO  and Digital input options installed. The first 5 watts are class A and it has discrete circuity, excellent parts quality, a great remote and a powerful toroidal power supply. The Naim 5i-2 was my second favorite followed by the Unison Research Unico hybrid integrated.
 BTY,
Tom