For in car Wi-Fi, I’d recommend the middle option. It’s much better with antennas, and the AC model is quite overkill.
Your NUC would be fine considering you shouldn’t have to transcode. I’ve tested 5 simultaneous devices on one of those travel routers and there was plenty of bandwidth and no stuttering with direct play on 1080p 10-20Mbps files. The only problem with the NUC is that you wouldn’t have a way to interact with it, you’d need to add a screen, keyboard, and mouse.
Honestly a laptop would be your best bet. It’s got a built in battery backup so it can keep going after you shut the car off, and it’ll safely shut itself down when it runs near the end of its battery. Not to mention it has a screen, keyboard, and trackpad built in. I posted this laptop on the discord just today. It’s around $211 in checkout. It’s got an 8th-Gen i3 (so it can hardware transcode via QuickSync) and would overall work great as a mobile server. You can upgrade the HDD to a 1 or 2TB SSD.