Hi Lilyheeler, welcome to BikeForums.
My advice is that the only way to know if cycling is for you is to give it a go. I'm sure that you've browsed the internet for information and have seen some supportive, encouraging documentation. Here a a few things that I would recommend:
Since your anxiety is initially focused on acquiring a bike, you should look for a bike shop that caters to a wide range of cyclists. Look for online reviews and local recommendations to get a feel for positive customer interactions. REI comes to mind as a good place to start. Having someone who knows bikes with you during your visit would be an advantage. Do you have a bike co-op in your area? If so, check them out first. Not only will they have experienced volunteers to help you with specific issues, they may also have some bikes available for you to try (or buy). Co-op membership tends to be widely diverse, so the term "typical cyclist" cannot be defined.
Certainly do look for someone in your area that you can ride with. Pairing up with a supportive person or group with experience will not only help you improve your skills but give you comfort while gaining your own experience.
Start riding in areas that will not have motor vehicle traffic. Do you have multi use paths, rail trails, etc. in your area? Of course they will have pedestrian and bike traffic to contend with; however timing your rides to avoid crowds should be easy.
I hope you move forward with your new interest. Let us know how it goes.