If you want a simple e-ink wifi screen I'd point you at the reTerminal e1001 [0] if that size works for you. It's the easiest to get started with. You can either keep it on power or use the deep sleep to get more from the battery. It really comes down to how often you want to update it.

The BTLE boards have just crazy higher battery time with no need for deep sleep which is why I'm moving in that direction.

~7.5" is the size I've been buying so far, the larger e-ink screens get pricey but I can't wait for a calendar-sized one to come down in price such that I can frame it and hang it on the wall. Lastly I'd avoid the color e-ink screens unless you know you need color, won't need to refresh it often, and it's not in your eye line. Color refreshes take way longer (~30s in my experience for a 5-6 color screen) and the flashing it has to do is obnoxious. Monocolor displays take <2s normally and a single flash. I got a color screen first because "why not?" and I got color, but the refresh was too annoying so now it refreshes once a day in a place that I'm not when it refreshes so I don't have to see it.

I also recommend you check out OpenDisplay for what you will run on the device: https://opendisplay.org/index.html

[0] https://www.seeedstudio.com/reTerminal-E1001-p-6534.html