First off welcome to the community.
Ankers brightest portable battery powered projectors are the Mars and Mars 2 pro. They are rated at 500 ANSI lumens which is roughly equivalent to around 5,000 regular lumens and will provide you with a decent picture during the day although not on a surface that is directly lit by the sun. ANSI lumens are the true measure of light output other companies use a high lumen count as a misleading marketing strategy.
I do not recommend projecting onto a horizontal surface but if you have to this projector has a mounting screw on the bottom that will allow you to mount this projector in in a horizontal orientation. Although you would have to mount this projector at a height of three feet or more, all projectors have a minimum distance to the surface you are projecting onto, and the closer the distance is from the projector to the projecting surface the smaller the screen size. I highly recommend projecting onto a vertical surface such as a wall.
@TechnicallyWell please share your valuable insight on how screen size relates to distance from wall/projecting surface.
The (Mars) and (Mars II Pro) will only give you about 3 hours of play time vs 5 with the Mars II. More light output or lumens = shorter battery life.
EDIT the Mars mentioned above is no longer available. To clarify there are four versions of the nebula Mars. The original nebula Mars, the nebula Mars lite, the nebula Mars II and the nebula Mars II pro.
Here is a video review of the Mars II by our very own @TechnicallyWell that will give you some idea of what the Mars II will look like during the day (video not shot during the day but was in a well-lit room). Just keep in mind the (Mars) and (Mars 2 Pro) are about 40% brighter than the Mars II.
Edit
Mars 500 ANSI lumens NO Android
Mars II 300 ANSI lumens WITH Android
Mars II Pro 500 ANSI lumens WITH Android