As I understand it, if you use a CRT, either via the analog I/O board or through Direct Video, and you don't engage the scaler, you have 0 display lag. What you see on the CRT happens at exactly the same time that you would have seen it on real hardware on a TV.
Depending on your controller and how it connects, you may have control lag, which is a different thing; this is how long from when you make an input to when the signal arrives so that it's visible to the core. On any USB controller, there's a 1ms poll rate, so your average response time is a half-millisecond. From there, you add any hubs, any wireless lag, and any controller lag. My DS5, for instance, apparently has about 2ms of control lag in wired mode, which is how I use it. There are a few that are even faster. There are many many that are much slower, especially in Bluetooth mode. The 8BitDo Pro 2 Wireless has 16ms lag in Bluetooth mode, for instance, a whole frame. And there are controllers that are even worse.
If you use SNAC, your input lag is about zero, but SNAC controllers only work in cores, they don't work in the main Mister menus. Because of that, I tend to think you should use SNAC only for lightguns. A fast wired controller is so quick that you don't gain much from a SNAC joystick.
Display and input lag are usually additive, but not always. If you have to see something and then react to it, they add. But if your reflexes are good enough and you can anticipate what will happen, they can sometimes run in parallel.
Ok, so, that's the best case; 0 display lag, possibly 0 controller lag, maybe 3 or 4ms if you have a fast wired USB controller.
If you engage the Mister scaler on the analog port, in the fastest/least compatible mode (vsync_adjust=2), you add four display lines of lag. This is largest on lower resolutions; at 320x200, if my math is right, that's about a third of a millisecond. At higher resolutions, it's faster. I don't think rotation adds any lag, although I could be wrong. I also think CRT filters are free, but I don't have actual hard knowledge of this. If anyone contradicts me, they're probably right.
You shouldn't need them on a CRT, but more compatible Mister scaler settings add more lag; vsync_adjust=1 is, I think, one frame of lag, and vsync_adjust=0 can be two. You want a display device that supports vsync_adjust=2 for best results. I believe most CRTs do just fine with it. It's flat panels that can be troublesome.
On any flat panel, you will add at least a little lag. In minimum-lag mode, the LG C2s add about 2ms to a 1080p signal. (but like 16ms lag for any 4:3 signal, so beware.) Most flat panels add at least 5ms, and 10ms is pretty common. TVs in modes intended for watching video can have very long lag times... those same LG panels are like 80ms lagged when not in Game mode. They're doing a lot of internal processing to try to improve the signal, and while they generally succeed, the output is way behind a CRT. This doesn't matter in the least when watching a movie, but you'll care a lot about it when playing Punch Out. And, again, your vsync_adjust mode will add lag as well... the Mister scaler is always engaged on an HDMI signal. Flat panels that can support vsync_adjust=2 are much better.
The output device you choose, in other words, the mode it's set to, and the Mister scaler mode it supports, all matter a lot. A CRT with no scaler running is the best you can possibly do.