I think it is sometimes common to feel anxious anytime you plan to purchase something that costs a lot of money. If the anxiety if monetary, I think that's a sign you need to do more research into the product you're looking at and the alternatives. If the question "is this the right option" is still in your mind, you're not ready to spend the money.
If the anxiety is centered around the actual purchase and process associated with that, it is probably some introverted part of your personality. People are, on average, average. So while many are extroverts, just as many will be introverts.
If the anxiety is centered around first-time gun ownership, perhaps you need to spend more time looking at what you're anxious about, checking out the local laws where you live, going to the range and renting guns, etc.
When I bought my first gun (not the first I owned, but the first I purchased for myself), I was coming from a childhood of shooting and hunting. I waited years not buying many of the things I wanted as an adult to put the extra money towards debt. Then when I was satisfied that my income was indeed truly disposable, I still spent almost a YEAR looking at options - handling different models, considering what I wanted to use that gun for, looking for the best deal - before buying it. I had no anxiety about it, because I was prepared, knew what I wanted and why I wanted it.