I currently run a variety of hardware to play EE. You don't need anything ridiculous, but I 'would' recommend a desktop if you can manage it. It will also depend on what else is running on it. I have the luxury of having an NWN EE computer that does precisely nothing else except play NWN, so its pretty weak in terms of its power. If I can make a decent, long term suggestion however, I'd recommend:
An intel i5 dual core processor.
8GB of RAM.
A decent hard drive but nothing overboard.
And a 1GB graphics card - a Nvidia 9 series would be good, probably, or a 1030. I currently use a 512mb graphics card, and its more than fine.
Find something that has those and you should be fine, if you're not putting it together yourself. A shop bought PC with a bunch of extra rubbish loaded into it will suck up more resources, so keep that in mind and boost what you need just a touch. Less stuff running in the background, the better.