I've owned the Audio Refinement Complete w/remote and it is a very nice piece at $650 or so used...the Sim I5 is well over your $1000 budget even used. The Creek 5350 can be had for about $1100 used and offers a lot of value and even two sets of spks. The Puccini is a good value by all accounts but I haven't listened to it. I went thru your same dilemma and each time returned to the Naim gear. The 3R can be had for about $650 and I recently purchased a used Nait 5 for less than $1000 with a pair of 17 ft NAC A5 cables terminated and a Chord DIN to RCA interconnect. Don't let DIN connectors and specially made speaker cable deter you you will NOT find a more musical, clear and enjoyable integrated even at twice the price.
The Naim line is known for build quality, PRaT and upgradability. You can later add amp, seperate power supply, and a CD but in the mean time you will enjoy the Nait immensely...the new 5 series offers a lot of the famed rythym and musicality with a dose more punch and detail.
Highly recommended
Jim