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.
At risk of sounding like a Nike ad, just do it! Find a character you want to dress up as and get started. If you need help there’s plenty of tutorials (both blogs and videos), books, and forum you can turn to for advice, especially if you’re doing something popular. Or you can do what I did and just muddle through it yourself. My first costume I bought what items I could, mostly at secondhand stores, dyed and altered a shirt and made some simple arm wraps out of cheap cotton. I had no idea what I was doing (and no sewing machine – do your hands a favor and use one if possible) but it came out pretty well and I’m still happy with it.
These days I usually make mine from scratch, finding a sewing pattern that is somewhat close and adapting it as needed. When I can pick up patterns cheap I look for anything that might be useful and stock up. I’ve gotten unused patterns for as little as a dime before, so even if I never use them I’m not out much. I like to let other people do work for me when possible. Secondhand stores can be good for base items and even for fabric, either by cutting something apart (one of my costumes is 95% bed sheets) or if you’re lucky even plain fabric (I once found a piece juuuust big enough and in the right color for an outfit I wanted to do).
Remember you can decide how true to the source you want to be. If something is outside of your skill level or too expensive to do “properly”, you can find a way to do something. I once stumbled upon a pattern to knit Rinoa’s duster, but painting or sewing the wings on a plain blue one works too. Or you can stylize it to your own tastes. My costumes never look great, my skills aren’t at that level, but I can do “good enough”. And you’ll never be sure what you’re capable of until you try.
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.