Honestly, VPS accounts are not intended for large, resource intensive websites with heavy amounts of traffic like Game websites. Such sites are best suited for our dedicated server packages. I will highly recommend considering a dedicated server for this purpose.
The game servers usually needs smooth, fast, and superb packages because of the heavy traffic and for this, dedicated server sounds to be the best solution.
I can see the point of having a dedicated server for a game website. However, I'm thinking that it is better to have a VPS than having a dedicated immediately because of the cost. You can upgrade when you already have good traffic and you are already getting income from the website. What do you think?
It also depends on the number of users who will be playing. (I can see a chain of "it depends" here.)
I would still stick to my former suggestion that a VPS is the best for starting a game server. You can get a one month package so that you won't pay big for a dedicated server. If the website did go well then there is no problem migrating to dedicated.
TBH, it depends upon the resources that game server will utilize.
Is there any way to break that down into estimates for those who are curious? I would love an idea myself. I game but I am not planning to resell and host anyone (at least anytime soon).
A Dedicated Server can support and host a game server installation because its CPU allocation and memory are far greater than that of the VPS Server. If you use VPS to install games, it will slow down the server.
Again, it depends on the type of games you will be serving. A browser game that only calculates the skills and weapon types then shows the result of a battle would use up very little resources. Most of these web-browser games have images and banner advertisements that eat up most of the resources of the server and not the actual game itself.
Now if you plan to host a game like an MMORPG or FPS games then you really really need (and I would personally recommend) a dedicated server. You might even need a custom package even greater than a dedicated server for this type.
This is an opinion of a gamer and not from a person that hosts games so I'm not saying that my words are the best answer. The others' opinions have good points and I respect them all.