These are the specs on your machine:
Dell™ Dimension™ 2400 Series 
Microprocessor 
Microprocessor type
 Intel® Pentium® 4 that runs at 2.2 or 2.4 GHz internally and 400 MHz externally, or 2.266, 2.4, 2.53, 2.66, 2.8, or 3.06 GHz internally and 533 MHz externally.
Intel Celeron® that runs at 2.0, 2.2, 2.3, 2.4, 2.5, 2.6, or 2.7 GHz internally and 400 MHz externally. 
L1 cache
 8 KB first-level (Pentium 4 and Celeron). 
L2 cache
 256- or 512-KB (displayed in the system setup program) pipelined-burst, eight-way set associative, write-back SRAM (Pentium 4);
128-KB SRAM that resides in the processor's core. The L2 cache runs at the processor's internal clock speed (Celeron). 
System Information 
System chip set
 Intel 845GV 
DMA channels
 eight 
Interrupt levels
 24 APIC mode 
System BIOS chip
 4 MB (512 KB) 
System clock
 400- or 533-MHz data rate 
Expansion Bus 
Bus types
 PCI 
Bus speed
 PCI: 33 MHz 
PCI connectors
 three 
PCI connector size
 120 pins 
PCI connector data width 
(maximum)
 32 bits 
Memory 
Architecture
 DDR SDRAM  
Memory connectors
 two 
Memory capacities
 128-, 256-, or 512-MB 
Minimum memory
 128 MB shared DDR SDRAM
NOTE: Between 32 and 64 MB of system memory may be allocated to support graphics, depending on system memory size and other factors. 
Maximum memory
 1 GB 
Memory type
 PC2100 (266-MHz) or PC2700 (333-MHz) DDR SDRAM (non-ECC)  
Drives 
Externally accessible
 two 5.25-inch bays
one 3.5-inch bay 
Internally accessible
 one bay for 1-inch–high IDE hard drive 
Ports and Connectors 
Externally accessible: 
Serial
 9-pin connector; 16550C-compatible 
Parallel
 25-hole connector (bidirectional) 
Video
 15-hole connector 
Keyboard
 6-pin mini-DIN connector 
Mouse
 6-pin mini-DIN connector 
USB
 two front-panel and four back-panel USB 2.0–compliant connectors 
Network
 RJ-45 connector 
Audio
 three back miniature connectors for line-in, line-out, and microphone 
Headphone
 one front miniature connector for line-out 
Internally accessible: 
Primary IDE channel
 40-pin connector on PCI local bus 
Secondary IDE channel
 40-pin connector on PCI local bus 
Floppy drive (optional)
 34-pin connector 
Video 
Video controller
 integrated Intel 3D Extreme Graphics 
Audio 
Audio controller
 integrated audio 
Network 
Network controller
 integrated 10/100 Ethernet 
Controls and Lights 
Power control 
 push button 
Front-panel power light 
 solid green for power-on state; blinking green for standby state  
Hard-drive access light 
 green 
Power 
DC power supply: 
Wattage 
 200 W or 250 W 
Heat dissipation 
 682 or 853 BTU (fully-loaded computer without monitor) 
Voltage (see your Owner's Manual for
important voltage setting information) 
 100 to 120 V at 60 Hz; 200 to 240 V at 50 Hz 
Backup battery 
 3-V CR2032 coin cell 
Physical 
Height x Width x Depth
 36.8 x 18.4 x 42.6 cm
(14.5 x 7.25 x 16.75 inches) 
Weight
 10.4 kg (23 lb) 
Environmental 
Temperature: 
Operating
 10º to 35ºC (50º to 95ºF)
NOTE: At 35°C (95°F), the maximum operating altitude is 914 m (3000 ft). 
Storage
 –40º to 65ºC (–40º to 149ºF) 
Relative humidity
 20% to 80% (noncondensing) 
Maximum vibration: 
Operating
 0.25 G at 3 to 200 Hz  
Storage
 2.20 Grms at 10 to 500 Hz 
Maximum shock: 
Nonoperating (half-sine pulse)
 105 G, 2 ms 
Nonoperating (faired-square wave)
 32 G with a velocity change of 596.9 cm/sec 
(235 inches/sec) 
Altitude: 
Operating
 –15.2 to 3048 m (–50 to 10,000 ft)
NOTE: At 35°C (95°F), the maximum operating altitude is 914 m (3000 ft). 
Storage
 –15.2 to 10,670 m (–50 to 35,000 ft) 
First of all, you can't even put 2 Gb of RAM into it.  It will only accept 2 512 Mb chips and those have to be PC2100 (266-MHz) or PC2700 (333-MHz) SDRAM.  You just can't buy 2 Gb.  So buy 2x 512 for a total of 1 Gb but get the right stuff.  Here's a list of what's available to you:
http://www.newegg.com/Product/ProductList.aspx?Submit=Property&Subcategory=147&Description=&Type=&N=2010170147&srchInDesc=&MinPrice=&MaxPrice=&OEMMark=0&PropertyCodeValue=523%3A8476&PropertyCodeValue=524%3A7861&PropertyCodeValue=524%3A7860Yes, one of those PCI video cards you selected should work but be very careful which one you choose as you only have a 200-250 watt power supply.  
One of these will likely be your best bet but you'll have to make sure that your power supply is the 250 watt version, not the 200 watt version (there should be a sticker on the power supply itself):
http://www.newegg.com/Product/Productcompare.aspx?Submit=ENE&N=2000380048%204025%201069609642%201068309611&bop=And&CompareItemList=N82E16814130289%2CN82E16814187041%2CN82E16814133233If you've got the 200W version then you'll need to settle for one of these:
http://www.newegg.com/Product/Productcompare.aspx?Submit=ENE&N=2000380048%204025%201069609642%201068309609&bop=And&CompareItemList=N82E16814139151%2CN82E16814102447%2CN82E16814139151REither way, don't expect wonders.  As others have mentioned, the technology in your sytem is old, even if the system itself isn't.  You're still going to have to turn down graphic settings in game, run lower texture sizes and keep background processes to an absolute minimum but, you will see a slight performance gain and you're only going to be in for about $50.
BTW, don't even think about upgrading the power supply to run a better card.  At that point you're just throwing money away because that first list of cards I posted is as good as you can go with this system.  At that point it's time to save the money for a new system.  You can get one built that will run AH just fine for around $500 and it will absolutely kill what you have now.
Good luck.