I'm a big fan of the Marantz PM7000N. It's the most flexible, best sounding, reliable integrated amp available for $1200. Factory rated at 80w/ch into 4 ohms, it drive most demanding speakers like my KEF LS-50s and Magnepan 1.7s easily. It also a streamer, and has above average DAC and phono preamps as well as both preamp and subwoofer outputs.
While I can't fault the Chronus Magnum III in its analog performance, it has no digital capability whatsoever, so a streamer and DAC are still required to meet the modern definition of an integrated amp. And at 4X the cost of the Marantz.
With that leftover change in your budget, you could step up to the $1000 class turntables like a Rega Planar 3 or Mo-Fi Studio Deck. And still have money left for a decent set of headphones or to take a chunk out of a speaker upgrade.
It's all in about Vp = SQ/Sum(C1 ... Cn) * K. Value Perceived equals Sound Quality divided by the sum of your component costs * K, where K is the qualitative enjoyment factor. K is what allows someone to rationally drop an additional zero or two on the price of their system. Quantitatively, a $100,000 system isn't going to sound 10X better than a $10,000 system, so a qualitative factor accounts for that. Negotiating the value of K is also the foundation of achieving acceptable SAF (Spousal Accepance Factor) levels.