Projectors and out door usage is like making a tractor compete against and F1 car on the track, they're not really designed to work that way.
In order to get one to work at dust outdoors you would be looking at a huge lumen count as this is what will be required to cut through the sun as it will just dilute the image making it look washed out. Now favorably, greens are easy for projectors to produce and in it's highest brightness mode, you might enjoy some movement on a smaller screen of around 70" to 80". You would still be looking at a lumens count of 4,000 and it would be better above that.
If you have a shaded area to place the projector and screen where the sun doesn't, again that will help.
But if you really wish to see what a projector will look like in your garden, buy a very bright torch and see what happens to the light when you shine it on a wall when the sun is out. You will see from that point that you really do need to think about how you are going to make it work. Budget is one area that will matter and maybe look at a secondhand until (although usually a replacement lamp will cost more than the projector selling at £300)