I have chased insects and butterflies in my backyard for many years, although it seems as if I see much fewer butterflies over that last few years, than I did ten years ago or so.
I loved the video of the focus stacking of spiders, lighted with speedlights strobing at 10 or 12 frames a second. Unfortunately, I don't think one can get speedlights to charge and fire like that unless the strobe is very close to the subject ( less than 6 or 8 inches )- which is great when you can do it with non motile subjects, as it is effectively a very large broad light source that close; but when I chase butterflies, which are very motile, my strobes are more like 2 or 3 feet away, and much of the capacitor is drained after just a few shots when out of doors in sunlight or bright shade. So I have not pursued focus stacking of insects - maybe I should give it a try. I do use speedlghts for fill flash frequently when chasing butterflies and insects, it really helps pop the colors and some nice highlights if done lightly. It can also allow one to utilize a much smaller aperture for greater depth of field.
For insects and butterflies, especially, I like the 180mm Macro lenses - mine is from Tamron, but they are also available from Nikon, Canon, and other manufacturers. More common, and less expensive, macro lenses are anywhere from 50-100mm, but I find them of less utility for wild, motile, insects as one has to get too close, and your subjects depart.
If one doesn't want to purchase a dedicated macro lens - a mild telepohoto with an extension tube is a great alternative. I have lots of images of butterflies and bees captured with a 100-400mm or a 200-500mm zoom on a 12 or 20 mm extension tube to allow the closer focusing needed for butterflies or bees. Longer lenses really allow one to try to find a pleasing background with nice bokeh to frame their subject within. Butterflies and bees are usually busy in dense flowers with stems going everywhere, so getting a nice background can be entertaining.
Like most photography, good lighting, good backgrounds, cool subject with great gesture, will lead to interesting images, usually. Luck helps a bit too. Sometimes I like to back out and show the insect in its environment, like a lion on the savannah too.
I shot this moth with a 10D in 2004 with a 24mm ( not a macro lens ) lens - my first digital DSLR, 15 years ago
Close up of a bee with fill flash
I love preying mantises, they are an apex predator, and they act like it - they look at me, absolutely unafraid I believe, and just go about their business, unlike most insects which run from shadows over head.
This preying mantis was shot 15 years ago with a 20D and a Canon 100 macro lens when I was just beginning to learn digital photography.
I call these guys, painted ladies, not sure where I learned that name, shot with a Canon 100-400 last summer, almost certainly with an extension tube. I love painted ladies, because they are so colorful and always available to dance with in the summer time in my backyard.
Here is another killing machine - a bee killer - as if bees didn't have enough issues these days, shot in the fall of 2006 in the flowering sedum, which always is full of bees when in flower. This is the only bee killer I have ever seen out there
Here is the end result of its hunt
There are lots of wild creatures in our own backyards, if we slow down and quietly begin to really watch what is happening there...
A tiger swallowtail with a Canon 100-400 and extension tube