We do not recommend particular projector models, but we have been very happy with Epson brand projectors. For best results the projector should have a minimum of 5,000 lumens for the brightness, be LCD technology for the color clarity (DLP projectors show yellow highlights too dark), and have an HDMI input in addition to a VGA input.
You will need the appropriate Apple adapter to connect your iPad model to the appropriate cable (VGA or HDMI), and then connect that cable to the projector. Or you could present wirelessly using an Apple TV.
For the screens the Da-Lite Deluxe Insta-Theater portable screens are relatively light and set up in a few seconds. The 48" x 64" size (80" diagonal with a 4:3 aspect ratio) or the 44” x 78” (90" diagonal with a 16:9 aspect ratio) are good sizes for most courtrooms.