This is a bit subjective, but personally I wouldn't do less than 1280x720. There are a number of 10.1" with HDMI that have that resolution or more. At 10.1 things get kind of small. I just don't think kstars/ekos will fit properly on 1024x600 or 800x480.
I do use ELECROW 10.1 Monitor at 1920x1080 for several years while in the field.
Small but completely usable.
Power it from a small Talentcell 12V battery.
-- Max S
ZWO AM5. RST-135. AZ-GTI. HEQ5. iOptron SkyTracker.
TPO RC6. FRA400. Rokinon 135 and other lenses.
ZWO ASI2600MC. D5500 modified with UVIR clip-in filter.
ZWO ASI120MM Mini x 2. ZWO 30F4 guider. Orion 50mm guider.
ZWO EAF x 3.
Yeah, anything smaller than 1080p would be really tight! But I'm actually not planning to use KStars and Ekos from it much, if ever. Just enough to get into the desktop and see that it is in fact booting OK and see what's up with the network.