Have you decide what the games will be built in? Flash is not accessible by any Apple device so probably not the best choice. Canvas has some really interesting games but the programming environment may not appeal to you?
Server-based games - as EastCoast mentioned - typically consume a lot of bandwidth. Also server threads tend to get overloaded. Have you considered using Node.Js for the server and the game wrapper? As Node.JS is event rather than thread driven and is asynchronous, you may benefit if your games become popular and there is high server demand. Node can be run on relatively modest hardware too.
Any game that has many sprites, animation, and or video will need a high amount a RAM. You should decide on your type of games, game platform, and server environment, plus whether or not the games connect to a DB. After that, you can develop a profile of the resources needed for each single game and also do some automated load testing to see when RAM, Threads, Processors, Cache etc become overwhelmed. Then you have a basis to determine how much RAM and the Hard Drive setup (RAID 10), and the processor/server hardware and hosting required to meet your game play needs. This could be a good case for looking at cloud hosting as you may need to start of modest but scale up easily. That is what cloud can be good at but it also can be very costly so you have to plan out your bandwidth to see if this makes sense over a shared or dedicated server setup to start?