So called 'serial port' programmers (like the JDM) are quite critical about the serial port they are fed from, requiring it to be above RS232 standard. These means they can be quite problematic, which is why my software WinPicProg only supports parallel port programmers - it's perhaps no coincidence that I offer support on WinPicProg, whereas the author of ICProg offers no support, and doesn't reply to most emails!.
So generally parallel port programmers are more reliable than 'pseudo serial port' programmers like the JDM, proper serial port programmers (that have an on-board processor) are fine, and probably most likely to work on all computers.
There are a number of parallel port designs on my website, they all work with either WinPicprog or ICProg (or any other compatible software), if you have a parallel port it's the best low cost way to go.