I've only heard the Rega Brio within your target items - a very solid entry integrated amp.
It's important to balance budget and any future upgrades into your selection. If you are merely looking to have an amp within the current system a PS Audio Sprout or other all in one like the NAD 3020 could be a good fit.
Another poster stated NAD products break after their warranty - that's not my experience and my stereo is on most of the time as I leave music on for my dog when I'm not home.