Amazon sells some aluminum utility scoops that are perfect for larger trees.
An excellent started set of sifters can be pieced together on Amazon. Start with these stackable green sifting pans. They come in 1/4", 1/8", and 1/20" sizes which is perfect for screening out fine dust and getting your soil appropriately sized for your bonsai. Very durable and they fit snugly into a 5 gallon bucket to aid in sifting. You can also use this plastic 3/8" sifter to get rid of everything that will be too big to even use as an aeration layer.
If you've got a lot of soil to sift, and you're looking for the absolute best, check out this $1,250 soil sifter from Bonsai Mirai. You can also find some how-to guides in this do-it-yourself soil screener forum post on Bonsai Nut, as well as an updated soil screener design that has some tips on where to buy the mesh and other items.
Small size is typically 3mm - 6mm, which is perfect for maximizing the 1/8-1/4" particle size.