It depends entirely on how many tracks you need to capture to some degree. I generally have the same approach, but for 6 or less tracks I'll just use my Zoom H6 (with 2xXLR extension adapter) for audio. For more, I pack my Focusrite, Behringer ADA8200 and old MacBook Pro.
I use splitters and DIs to "T" out of the lines to the board, so the house doesn't have to change what they normally do, and I don't rely on the board having available sends for each channel. It's a dry signal, so I have to mix it to sound as close to the house as I can, and I will almost always include a tiny bit of the camera audio for ambience. I mix that, then sync it to the video. This usually means I'm getting a direct signal from a guitar with a pickup. (I can supplement with a shotgun mic to get more acoustic sound, but that generally only works if it's a good stage and the performer holds still!)
If you're talking a full band, that can get complex and you'll probably need a rack of splitters - I haven't had to do that yet, since the only band I did only mic'd vocals and one guitar, with everything else having its own amp (or none, in the case of drums). Then you'd need to mic up anything that wasn't going to the PA that you could capture.
I am *not* a videographer but will set up a camera or old camcorder somewhere when I can, since it seems everyone wants video - this is purely for "proof-of-concept" stuff, and I can tell you that doing both by yourself can be difficult, since it's hard to monitor both at the same time, and if you're watching the audio, and the camera goes out of focus or gets bumped, you've lost a bunch of video. Same thing if you're watching the camera (and consumer level cameras have pathetic monitoring capability IMO for this kind of stuff, not to mention they eat batteries if you are monitoring/recording for a long time).
Here's a guy I recorded last week - old camcorder at work - static shooting from the table where I was sitting.
YouTube