Of the three components you mentioned, you cannot use the Classe because it is a power amp only, not an integrated amp. To make a power amp function you would still need to purchase a preamp, which has controls (such as volume) and inputs to connect sources.
The two integrated amps listed could not be more different. It is a choice between a minimalist tube (valve) unit and a feature-packed solid-state unit that has many digital connections. If you want great flexibility and do not need HDMI connections, the Rotel would be an excellent choice.
Note that I have not heard any of the stated components, so I cannot comment on sound quality.
Music room: Cary SLI-80 tube integrated amplifier, McIntosh MA6500 integrated amplifier, Quad 99 preamp, Quad 909 power amp, Acoustic Research AR9 loudspeakers, Yamaha CD-N500 CD player, Teac UD-503 DSD DAC, Phase Linear 8000II linear-tracking turntable.
Theater room: Panasonic 65S60 plasma television; Yamaha RX-A2020 (preamp section); Adcom GFA-5503 and GFA-5400 amplifiers; Polk LSi25, LSiC, and LSiF/X loudspeaker system; Velodyne FSR-18 servo-subwoofer.