FYI: I think all of these are higher than the minimum.
Right now, I am using an 11 year old laptop with 1.6ghz and 768 mb RAM. (It still works because it was originally a high end $2500 list price laptop back then.)
I had some problems at first, but they were caused by a bad USB port.
I am using a Hauppauge USB TV tuner which has its own AC power (to offload the aging USB ports of the laptop) and an external drive hosted by my router (which, unlike the laptop, supports using a 3TB drive so that I don't have to monitor the disk space).