Who is providing the cheapest CDN today?
Akamai is certainly out of the question, as it targets big enterprise customers.
Amazon CloudFront? Google? Azure? CloudFlare?
Choose a CDN with a global presence having servers in countries that you foresee your visitors to come from.
CloudFlare is one such CDN anyone can try. Try out the free service and see if the paid plans which offer more enterprising and interesting features such as Railgun is of your interest.
If your services are hosted in any of the cloud provider, then you can opt them as one of the choices, but I don't recommend if your services are hosted elsewhere. These CDN services in the cloud provider normally integrate better for their other services.
To TS:
In order to make CDN advantages to you, you will need to have good understanding on Web Caching. Otherwise, you wouldn't reap the benefits of CDN effectively. Also you will need to understand the caveats of caching and how to work with and around it.
I also read about MaxCDN but I have not done much research on it and have not used it before. You can go take a look