Well, I'll judge off of my IBM Thinkpad A21p, a high-end desktop replacement laptop that originally cost $2000 back in year 2000...I got it used on eBay for $200 though.
1.) Storing and accessing pics should be no problem for pretty much anything. You'll obviously want something that has a USB port to connect cameras or flash card readers, or even printers. An added bonus would be a built-in SD card or other card reader. Something you'll want on a photo laptop is a high resolution screen that is fairly large. My laptop has a 1600x1200, 15.4" 4:3 display, and it is great for pictures because the high resolution makes them look great. A TV-out card/port also helps because you can show slideshows on big TV's. My laptop has a TV (S-Video) output. A large, high res screen is also a plus if you're editing pictures, as a big screen gives you plenty of room for tool boxes as well as a decent picture editing window.
2.) 3d games <2003. I have a game that I play often (Star Wars Jedi Knight: Jedi Academy) from 2003. It runs fairly well on my laptop (which has an ATi Rage Mobility 128 M3, 16MB, AGP2X graphics chip). Games use all the hardware together though, and my laptop originally had 128MB RAM. The hard drive went crazy as it used a pagefile, so I upgraded to 512MB and it ran much smoother. For games above JKA (which is based on the Quake 3 engine), you might want a step-up from the Rage, such as a Mobility Radeon or GeForce4 or greater.
3.) Wireless Internet. That's the thing. My laptop did NOT come with anything but and integrated 56k modem. I had to buy an external WiFi and Ethernet card, but it's easy to plug in and go online with either one, so no big deal. Most laptops have PCMCIA/CardBus slots to use WiFi or Ethernet cards in, and most newer laptops have built in mini-PCI or integrated WiFi and Ethernet cards.
As for what you need, I'd say better than my laptop. Though mine can do most of that, you'll get better performance out of something newer. I don't think you'd need much newer, but a 1.0GHz or higher CPU, 512MB or more RAM, Radeon or GeForce4 or greater graphics card, at least 2 USB ports (mine only has one) and high resolution screen help a lot.
As for Brand name (you mention Dell), it is unimportant. Brand name doesn't affect anything about the PC, as all PC's use either AMD, Intel, or VIA (only in cheap PC's) CPU's and AMD, Intel, nVidia, etc chipsets, and either Intel, ATi, or nVidia graphics. The manufacturer isn't as important as the parts in it.
I'd check eBay for used but good condition models, as you may get something fairly nice for around $300 or so. You can also buy new, but the price goes up by a lot.
