ATI Mobility Radeon HD 4200(128mbVideoMemory) vs Intel GMA 4500M( 1695mbVideoMemory)?

Do not buy an HP. Do NOT buy a dell (unless you have 3 million dollars to waste). Buy an MSI if you want affordability and power. it's a lesser known company but they make AMAZING laptops, fairly durable and well-priced. Make sure you get something with DEDICATED graphics. I would suggest at least 256 mb vid memory. The intel video you have up there is what is called shared vid mem, this will make you want to throw it off of a bridge if you ever even hope to game. My advice is get something with a nvidia gpu, something at or above the 8200 g level, with at least a 2.0 dual core and 3 or 4 gb ram.