From: United Kingdom
Even for a really basic machine (unless specifically looking for a really quick'n'easy build), I'd be reluctant to go with onboard graphics ... the same memory bus, for the CPU, for DMA, for the memory access for screen refresh, and for any accelerator functions in the graphics.
The Celeron (assuming the latest share the same characteristics) has a reduced cache, so it's more likely to notice the missing memory bandwith ... these days, losing 64Mb of system ram to graphics doesn't hurt, but losing all, the memory accesses that the CPU doesn't get, really hurts.
The "Unified Memory Architecture" is as EVIL as it ever was, and the fact that these days, the graphics processor unit is expected to do more than just display what the CPU gives it, makes it even worse.
Of course, if it DOES have an AGP slot, you do have the option of upgrading the graphics if the use of the system changes - AGP slot-less onboards are truly an abomination - and system builders like DELL use them!