People about Cosplay...
Honestly it’s all about what you personally find to work best, but for me I put on the costume first, or at least part of it.
For starters, it makes sure that the makeup doesn’t stain the neck hole of your costume, if there is one. This way all you have to worry about is usually powder fallout and that can be cleaned easily. You could also cover part of your chest with a towel like a bib if you’re really worried about stains.
If you’re putting on a wig it also helps to not dirty that or have it in the way of your work.
Also I find that the makeup tends to look better with the pieces around it. Makeup that is over the top or has unnatural aspects will sometimes look really silly with your normal hair and clothes, so to save the worry that you’re not doing it right, it helps to have the rest on. Especially when the wig comes on it all comes into place and you can do needed touch ups.
I often will only put on half the costume though. For example if the costume involves a jacket, belt, jewelry, etc that I can put on without touching the makeup, I’ll wait until the end. This also helps the makeup since costume pieces might not be made with full mobility in mind and can weigh you down or prevent movement.
Costuming has been around a long time: we find artifacts from tens of thousands of years ago where they were used to portray a being or spirit. Often those who played the parts in costume were held in high regard.
A little time with kids or a parade group reminds us all how much fun people have – let alone when there is a formal play being staged. Costuming is fun; it’s fun for people to pretend, but it should be understood by all that it’s to be pretend. Problems come when the “role” gets mixed up with one’s being; the role defines the person instead of the person defining the role.
As Jack Nicholson famously said to Michael Keaton as they were suiting up for their roles in Batman (1989): “Time to let the costumes do the acting.”
When the role is more than the person, that causes psych problems.
I’m going to address this question from a different viewpoint. Why is cosplay popular amongst those that do it?
There is the factor of honoring the source material/fandom that you love. There is the creative outlet. Then there is the sharing of the work with other fans and making new connections with like-minded people. Getting complimented for your work can create a sense of accomplishment, as can having a photographer ask to take your picture. A three day event like a local comic-con or Anime/SF/Fantasy Convention can be more rewarding than a two week vacation in the tropics, to some people.
This all has a spillover effect, those that aren’t doing it, see the results and fun that those that are having and want to do it themselves next time. This keeps the world of Cosplayers growing at a currently staggering amount. I’m staff on a 2,200 person Anime Convention and we are constantly amazed at the ~60% cosplay attendance.