Sony's A6000 works perfectly well, but I recommend you also grab a NP-FW50 dummy battery as it will drain the battery even when plugged in via USB over time.
If you want better sound, grab the A6600 which can also sport the XLR-K2M microphone adapter.
Regarding HDMI capture: the Blackmagic DeckLink card series works just fine in a Thunderbolt case (at work I run a 2x A6000 system + external HDMI input).
And if you wanna save some cash, any $20-25 hdmi to usb capture card will work just fine. It won't give you uncompressed video, but you won't need it for this use case.
I've been bitten in my ass lots of times by these things. Random crashes, overheating, dodgy connectors that don't tolerate even the slightest movement... thanks but no thanks, the cheapest DeckLink clocks in at 150$. Downside is you'll also need a Thunderbolt PCIe case, but eh. It Just Works (tm).
