Looking for a little more than the original but still have a tight budget? The RX100 IImight just work, because its use of the BIONZ X processor and a newer back-illuminated 20MP 1″-type Exmor R sensor help boost image quality across the board. It also is the only option with the Multi Interface Shoe, meaning it can accept the optional FDA-EV1MK EVF, a real flash or radio trigger, and even an optional microphone for better audio quality in video. Other nice tweaks include a new tilting screen, though limited to 90° up and 40° down, and built-in Wi-Fi with NFC. It does keep the same 28-100mm lens as its predecessor.
You could say that the RX100 III is when everything changed for the series. It was the first model I purchased because the massive number of changes and improvements were just too tempting. For pros looking for a solid pocket camera, this is where I would recommend they start. The use of a better and faster 24-70mm equivalent f/1.8-2.8 lens, Full HD video getting boosted with XAVC S and S-Log2 for pro-level capture, and a pop-up 1.4m-dot EVF puts the III in a whole other league compared to the earlier models. Also, for vlogging and selfies, this model introduces the 180° tilting screen. There is even a built-in ND filter to help handle the brightest scenes and more control in video. It does lose the hot shoe for a slimmer profile.