Look out for some off-lease stuff. I've had great luck with Lenovos but mostly because a forumite here had a bunch he was offloading.
Something like this with a cheaper vid card would probably do the job easily. You could go even cheaper too.
You can find any manner of Core i5 off-lease towers or mini towers from dell, lenovo, etc. for probably about $100 on ebay. Pop a reasonable graphics card in and you should be okay. I rarely run dreamcast so I can't exactly tell you "such and such a processor will run this game perfectly" or whatnot, but you've got plenty of options.