Once you have your Managed WordPress hosting account established you can then upload the theme of your choice in your WordPress dashboard.
Themes come in zip files that you don't open -- you upload that zip file via your WordPress dashboard (Appearance > Themes > Add New > Upload Theme).
Managed WordPress hosting also gives you a temporary domain to work with until you have your new site ready to go. The old site is then live until you are ready to move the domain to your new hosting/site.
Stay away from free themes. They are not well supported and tend to not keep up with WordPress or security bugs/threats. So gravitate toward premium themes. Keep in mind that when you buy a theme you own it. That is why going through the theme demo with a fine tooth comb will let you know if that is a theme you can use for your project.
I have an article that may help you know what to think about before you invest in a theme: Choosing the Right WordPress Premium Theme
"Be a voice. Not an echo." ~ Anon