First of all, hi and welcome to the forums
As for your eBay suggestion, that'll probably be your best bet unless you were willing to build it yourself. Are there any pcs in particular that you've been looking at?
As for the quad core vs i5, well an i5 processor is a quad core processor, so you may have to be more specific with your question
P.S. I forgot to mention it above, but I too would most likely go for a desktop over a laptop