>>4115695Just get yourself a Ricoh GRIII (28mm equivalent) or GRIIIx (40mm equivalent). They're a little bit more than your price range but they take awesome, professional quality photos photos (check out Sean Tucker's Instagram and his tutorials on Youtube). Plus, a Ricoh retains quite a bit of its value so even if it costs more upfront you'll also be able to recoup more of the cost if you sell it.
https://youtu.be/xmV5FfSaEcw Fujifilm XF10 is also a, in some markets, cheaper alternative; but it's not on the same level as the Ricoh.
https://youtu.be/AmPzP9OJIhU A Sony A6100, A6400 or ZV-E10 are also small:ish with the kit lens and you'll be able to pick one of them up with a kit lens for around $500 when they go on sale.
https://youtu.be/a03o3B1S7_k DON'T get anything smaller than an APS-C sensor, you're just gonna be disappointed. The difference between say a 1" sensor and your typical phone pre and post -processed with AI algoritms isn't huge and there's even phones with 1" sensors now, whereas an APS-C sensor is more than twice the size of a 1" and will subsequently let in more than twice the light of the best camera phones. If you're not going for an APS-C then you might as well take photos with your phone and touch them up in Lightroom and Topaz Denoise/Sharpen/Gigapixel - the results will be almost identical.