That is quite a lot of connections!
Providing that everything does not connect at exactly the same time or your application allows for queuing / a tiny bit of latency, I do not really think you will have a problem with regards to CPU or memory as long as you take an average modern box (Minimum Quad Core, 4-8GB memory), but I think you will want to take a look at serious Intel networking gear and tweaking Windows Networking (For example look here, but that list is quite old and I am not sure how many still apply).
If however you really want to prepare for big loads of connections, the real thing to look at is clustering your environment - however, if this is a custom written application, you may have a little trouble.
Also, for that amount of connections, you will need to look at upgrading your entire infrastructure - for example, faster/powerful routers/switches.