Native resolution is the normal resolution of the CRT monitor or laptop LCD screen. For monitors, there are a number of possible settings, but in laptop LCD screens, the number of pixels making up the screen defines inherent resolution. You may want to think ahead about what your next computer will be and if the planned projector will handle its display resolution. Today's projectors will handle their native resolution and also usually compress the next higher level resolution. Compression uses a software program to determine the best way to display a higher resolution.
Modern methods are so effective that it is difficult to tell if an image has been compressed.
It depends on the ability to control the location's ambient lighting as well as the required image size. If the room size increases and lights cannot be dimmed, the projector may need to produce 2,200 or more lumens. It depends on the application. If you travel a lot, your projector should be small and lightweight. If the projector will be stationary or ceiling-mounted, size doesn't matter as much.