Be honest with yourself about the split, and the answer follows from it. Mostly two-channel music: stereo integrated. Regular movies too: AVR, possibly with a stereo amp added later.
At 80% or more music in two channels, a stereo integrated amplifier at the same price will usually sound better than an AVR. The reason is where the money goes. An AVR at a given price funds seven or more amplifier channels, video switching, decoders and room-correction hardware. A stereo integrated at the same price funds two amplifier channels and a preamp stage, and nothing else. Two excellent channels beat seven adequate ones when only two are ever working, and the power supply behind those two channels is usually much more generous.
Where the AVR earns its place is when movies are a regular habit rather than an occasional one. Bass management (sending the low frequencies from every speaker to the subwoofer at a crossover of your choosing) is something an AVR does as a matter of course and most stereo amps do not do at all. Room correction, a centre channel for dialogue, HDMI switching with eARC from the TV: none of that is optional once you take films seriously. Speech intelligibility from a phantom centre in a wide living room is not something I would sign up for.
The middle path many of our customers take is the AVR for theatre duty, with its pre-outs feeding a stereo amplifier for the front pair. Music runs through the AVR's preamp into the stereo amp; films use the AVR's processing and the same front speakers. It can be added in stages: AVR now, stereo amp when the budget allows. The condition is that the AVR has pre-outs, so check that at purchase, not afterwards.
Where the rule stops mattering: small rooms, modest speakers, background listening. There the difference between a good AVR in stereo mode and a modest integrated is real but not large, and convenience wins.
Ten-minute call, decided permanently. Tell us the split, the speakers and the room, and we will say which of the three paths fits, and whether the stereo amp is a now purchase or a later one.
Not sure what fits your room and budget? Share your room size and budget on WhatsApp. It is a two-minute answer with a floor plan.
