I would avoid that particular eBay PC as it isn't very upgradable. It has a mATX motherboard with only 3 expansion slots, the installed graphics card of which is likely to block 1-2 of those already. Also, it has only 2 RAM slots, both of which will be filled with the pre-installed 4Gb RAM. Granted, you may never need to upgrade these, but wouldn't you like to have the option?
The case & PSU will be very basic too - that's why no brand names are mentioned. If you need to upgrade the graphics card at some point in the future, you're most likely to upgrade these as well at additional expense.
However, if it's going to be a use-once-and-dump-PC (i.e. no upgrades for the life of the machine), then it may be OK. G