You would need a computer with at least 4GB of RAM, and a disk large enough to run the software and some swap space. I suggest at least 4GB of swap space. CPU generally doesn't matter, unless it affects your challenge times.
Most people just rent VPS instances in the cloud. Some providers are better than others. I have a few from the same provider, in different locations... one runs on 4GB with no swap with no issue. Another needed me to upgrade to 8GB to keep it from crashing. Your mileage will vary.
While I do agree with everything said here, I would like to add that number of cores is also very important. In a single core instance with 4gb of RAM you most likely won't be able to run the high diff challenges (appx 1/10 will fail based on personal experience) leaving you out of 1/10 of your potential earnings. So be on the lookout for that as well.
