How to make a brand new WordPress blog a subdirectory of a hero-hosted Rails application?

I currently have a Rails 4 application hosted on heroku under "my-app-domain.com". My ultimate goal is to host a WordPress blog hosted elsewhere (like Arvixe) under "my-domain.com/blog" for SEO purposes.

Additional Information:

• The blog will be brand new.
• My Rails 4 app is hosted on heroku under "my-app-domain.com"
• I bought hosting from Arvixe for a blog and created a dummy blog under "some-other-domain.com". I am using Arvixe, but since the blog is going to be completely new, I can change the hosting service if necessary to achieve this.

Questions:

• How can I achieve this?
• Do I have to first create my blog as a subdomain of "blog.my-app-domain.com" and then use the reverse proxy gem to change it to "my-app-domain.com" ./blog "?
• Do I need to buy SSL on both Heroku and Arvixe for my entire site to work under SSL?