Preface: I have an idea for a game. I already written down the concept of the game. It's not going to be a browser game, it will be a downloadable game for both desktop then for the mobile app. I plan on creating the forum for the game while the game is still in development. The type of game I want to make is a multiplayer online turn based strategy game. Here are a list of questions I have to ask about the development of the game:
1. Who do i need to hire on my team for the following:
a. Designing the official website for the game.
b. Designing two official forums for the game, one for the U.S. and the other for the rest of the world.
c. Designing the game's appearance such as, menus, loading screen, health bar, avatar placement, etc.
d. Creating the game mechanics
e. Creating the program the game runs on.
f. Providing servers for the game to run on since it will be online and accessible to people across the globe.
2.) What would a reasonable budget be on game thats turn based, but not fancy like hearthstone?
What you wrote in your preface does not match items 1 and 2. If you have to ask question 1, you probably aren't in a position for question 2.
Even so, some answers:
1. You need to hire a business developer or experienced business manager first, or spend a decade or so getting real work experience so you know these.
1a. Job title is a probably an artist or designer, or in a pinch someone with moderate graphics editing and web-programming talents.
1b. Job title is probably web developer or any computer programmer. There are hundreds of existing forum programs. Having a US and Non-US version is easily supported with many forum systems. Nearly any competent web developer can set you up with one of these, if you can't manage to do it yourself.
1c. Job title is UI designer, sometimes called UX or User Experience designer. Also an art director, or UI artist if you must.
1d. Job title is probably game designer and family (junior designer, character designer, level designer etc), producer, probably with a programming discipline helping to ensure the mechanics are workable.
1e. Job title is programmer, lead programmer, technical director, and similar.
1f. Job titles include network programmers, network engineers for the hardware, IT, and similar.
2. "What would a reasonable budget be" depends on far more than you asked here. Development costs for people living in New York City or in San Francisco will be far different from people living outside Moscow Russia, or Durango Mexico, or suburban India.
I'll guess anything from around $200 if you do it yourself and pay as little as possible with very cheap hosting and a tool like GCCG, to something around $40M if you are doing things with professional developers doing professional work at professional wages and professional quality living in an expensive city.
If you were discussing contract rates with our studio, based only your descriptions and questions you'd asked, I'd guess it is a project on the order of $25M. Professional quality, but still be prepared to invest another $30M marketing it if you want it to succeed, plus another $20M or so post-development. Hopefully you'd also have done some market research before you've sunk your $80M into the full project, although I wouldn't particularly care about that.