I wouldn't waste your time with a projector for use outside unless it is pretty dark. I don't have experience with more expensive models but the budget ones are pretty bad with ambient light. I can't imagine even a more expensive one will solve the brightness issues. You're probably better off just buying a cheap flat screen for tailgating. Here's an example comparing both options.
720P projector with a dim lamp on with no outside light.
720P projector no lamp on and no outside light.
1080P on cheap 4K TV with lamp on and no outside light.
1080P on cheap 4K TV with no lamp on or outside light.
Maybe an expensive projector will be much brighter but you will also have to deal with much more light outside. That 4K TV is just a cheap $200 58" Onn TV that I got on Black Friday. You find a deal like this one and you can probably have everything you need for like $500-$600 if you aren't against buying a cheaper brand.