Choosing which animal most closely aligns with the character traits you value is a choice rooted in a personal sense of integrity and moral code. Generally, there is no right or wrong meaning associated with a particular animal when worn as a tattoo. However, if you're portraying an animal in a style characteristic of a distinctive stylistic school or tattoo culture, you should know the meanings attached to it. If you wish to remain true to a specific style of tattooing, you should seek a tattooer who is skilled in both the design subtle nuances of meaning associated with positioning and color.
Deciding to get a tattoo is a big deal, regardless of whether it's your first time under the needle or not. But for a tattoo virgin, the stakes are arguably even higher when it comes to picking a design and spot that won't be hated later. Classic wrist tattoo ideas are always a great place to start for inspiration, IMO, although what you choose to ink is entirely your decision.