Welcome to the forum.
It's hard to say, but seeing as you need a BNet account for each copy of Diablo 3, you could always start up four new BNet accounts (three you're going to keep and the fourth being a throwaway) and see how the D3 trial runs on those. Unfortunately, trials cannot play with retail accounts (although that may have changed), so you would need that fourth throwaway BNet, and when the time comes you can just upgrade three of those four to use with your main account.
The trial isn't the best way to gauge performance since the RoS expansion brings some better looking areas which are a bit more taxing, but it will give you an idea. I mean, if you can't run four copies of the game from level 1-20 then you're certainly in need of upgrades, but this all depends on what resolution and framerate you expect to be playing at.
My guess would be that, right off the bat, your RAM is going to be a limiting factor with four game clients, and increasing to 16GB sooner than later would probably be best. After that it'd likely be your CPU, and then your GPU, but I'm just guessing and you can always monitor your hardware yourself to see what the bottleneck is.
It's safe to assume you're going to be using ISBoxer since no other software, that I know of, is capable of multiboxing the game due to the mouse broadcasting required, but with that said, you can either launch the executable directly, or go through the launcher--either method is acceptable and launching is mostly automated (in a not-against-the-game's-rules way).
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