Need advice on outdoor projector

Hey everyone, looking for a good quality mobile projector.

I just moved into a new place and we have a nice outdoor area (~20x35 ft) with a white fence around 2 sides, and a large 2 story brick wall on one. I was thinking that it was a fun idea to buy a projector to be able to invite folks over for movies, NFL and UFC fights, especially since going to anything this year is looking less and less likely.

Looking for some good ideas on reasonable outdoor projectors. They will be moved inside when not in use.

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Maximum Budget: $600

Screen Size: n/a - 6ft?

Distance from the back wall or preferred mounting position to screen wall: ~10ft

Seating distance to screen: 10-20ft

How will you mount (ceiling, rear shelf, table)? - Table

Usage (Movies, TV, Games, Sports, etc): Sports + Movies

Room Type (Dedicated, Mixed use, Living room): Outdoors

Light (Ambient, through lighting, or light leakage from windows): Outside

Room Colors (Walls, Ceiling, and Floors): One brick wall, the rest, white fence