Everything but the last, get whatever Dell or HP or Gateway has on sale for cheap. More power than you'll need for those tasks.
For gaming, you definitely want a P4 or AMD processor. Don't get a Celeron if you want to play games. Video card is also important, I wouldn't want anythign less than an ATI 9600 or nVidia 5700 series card if I were playing HL2. If you could get into the ATI x600/x800 series, or nVidia 6600/6800/7800 series, so much the better. The card is something you could probably add on later, too, just make sure you get a computer that has an AGP 8x or PCI-E card slot. I am looking at moving from a 9600XT to a 6600GT right now, the new card is going to cost about $140. Also for gaming, 512MB RAM is the minimum I'm reccomend.
For the laptop, HL2 is pretty much out unless you want to start talking in thousands of dollars.