We are wanting to upgrade his computer to atleast a 256mb video card or 512mb video card, wanting to keep the price down since going somewhat expensive would be better spent on a new computer. Also not sure but he'll probably need a new power supply and the case is a "slim" model which adds to the complexity. Please could someone recommend their thoughts and the item/s (preferably on Newegg) that he would have to buy to upgrade his computer?
If it were me, I'd find out what standard it uses (knowing dell it probably isn't a standard ATX power supply plug) and then just transfer the contents to a real case and a new PSU and overclock.
But that's being optimistic. It is a dual core, and it is pretty good. You may be able to get away with sticking in a 4670 or 5570 as it is. Anything more than that, and you will need a new PSU definitely. Much more than that and you start possibly hitting the top of what that CPU can do without overclocking.
Use this http://extreme.outervision.com/psucalculatorlite.jsp
and see what it is with the 4670 added, it'll probably be fine. IIRC the 5570 uses the same or less power than the 4670 and either will be a huge boost and this is probably the best solution. The 5570 is also low profile standard, so it has a better shot of fitting in the case.
You'd have to get a low profile card which is pretty crappy way to start out.
If it were me... I'd gut it out of it's current case by a new case and install the components in that. This will give you more room and better upgrade options in the future. ALSO and this was a big ALSO, please keep in mind that these budget pc's aren't the best of components, so your power supply will most likely fail when you take it to the limit with a decent GPU. I would seriously consider just selling it on ebay and building a new one. If you can't build one yourself, find someone who can. Installing a gpu in a slimline case isn't impossible but it may require the use of a dremel.
... It says on the site that it's upgradeable, and it may be a problem for cards that need a PCI-e power plug but neither of the ones I mentioned do. Not only that, the 5570 IIRC uses less power and is somewhat faster than the 4670. And comes with a slim connector to begin with.
On top of all that while I like the idea of moving to a real case, this is a dell we're talking about and there's no way to know if the power its using is standard ATX plugs and power or not.