Hi bookworm86, I’m not sure there is a “best” way to observe–you’ll likely get different opinions from various folks. I like to challenge myself and get my photos without capturing the species. This avoids some problems (e.g. photographing through a glass jar), but creates ones too (getting a decent photo of a fast-moving insect or maybe missing the photo altogether!).
As far as cameras, there are many choices out there. A key question to ask yourself is whether you’re mainly just photographing smaller species (= a camera with good macro capabilities is obviously key), or more of a mix. Your budget is also obviously important, but there are many people here who get wonderful photos with very basic/inexpensive cameras–including the cameras that are onboard many of the phones now. There are also macro “add on” devices for phones that some people have had good luck with. Steve Ingraham writes about nature photography with consumer-level DSLRs that might be worth checking out too (https://psnp.info/psnp_/)
And if your interest is insects, I agree with cmcheatle that a night attraction setup can be an easy/fun way to bring in a variety of insects for you to photograph. If you do, definitely consider using a MV (mercury vapor) light now and then, or use both a MV and a UV (blacklight). Your experience depends a lot on your location, time of year, etc., but I never really had great luck with just the UV blacklight; adding a MV light really brought the bugs in! The trouble is that MV lights are becoming more difficult to buy; I bought mine through BioQuip (bioquip.com).