Does animal print make you look like you're trying too hard? Only if the dress is doing all the shouting on its own, with nothing plain near it to let it breathe. The print needs quiet company, not a second loud thing standing next to it.
I keep mine away from anything else with a pattern, that's the one rule I actually stick to. A leopard print dress wants a plain coat over the top, a block colour bag, shoes that don't try to compete. Denim jacket on top works too, oddly, it takes the dress down a notch and makes it feel like something you'd wear to pick up a prescription rather than make an entrance. For jewellery I go gold and simple, nothing with its own texture fighting the print for attention. Occasion wise it's more forgiving than it looks, a jersey animal print dress with a bit of give in the fabric does a Sunday lunch as easily as it does a leaving do, and I've had the same one on for a wedding and then, four months later, a work thing I was dreading, both times with different shoes and nobody clocked it was a repeat. Autumn and winter suit it best to my eye, something about leopard and tiger prints sitting next to jumper weather and darker boots feels right, where the same print in bright summer sun can look a bit costumey. As for colour, the classic tawny brown and black leopard print is the easiest version to live with by miles, it goes with nearly every shoe and coat you already own, while the all black snake print or a cooler grey toned animal print reads smarter and quieter if you want it for something a bit more formal. Bright red or pink based animal prints are lovely but they're a one season flirtation, not something you'll still want out in March.
Feel matters more than people admit when they're buying these. A stiff, shiny polyester print sits away from the body and looks like it's wearing you, whereas a softer jersey or viscose version moves when you walk and skims instead of clinging, and that's the difference between looking confident and looking like you're in a costume. I bought a cheap satin one years ago that crackled faintly when I walked, actual static, like I was announcing myself before I'd entered the room. So when you're next looking at one, put your hand flat against the fabric before anything else, if it's got proper drape and doesn't feel slippery or papery, that's the one worth trying on.