while I haven't personally owned an eMachines, and the last time I bought a computer at retail it cost nearly $5000 and eMachines was considered junk at the time (and they still cost $700+ for a system about 1/3rd the power of what I bought)
BUT
I'd suggest two things:
The T6212 as every one seems to be suggesting it, and from the specs i've seen it looks very nice for the price
but my personal choice would be to extend the budget about $125 and build it yourself
configured at www.newegg.com, $1004.93 w/no monitor, shipping, KB, mouse or speakers:
Athlon64 3500+
ATI Radeon X600XT
1GB PC 3200 DDR
7.1 sound
250GB Maxtor SATA-150 Hard Drive
WindowsXP Home Edition w/SP2
DVD/RW Drive
DVD-ROM Drive
Antec 450W PSU w/Antec SOHO File Server case (it's REALLY expensive ($139.00 for the case/PSU combo, which imo is great considering the PSU boasts better rails than the NeoPower, and the entire thing costs $15 more than NeoPower (and NeoPower doesn't have a case w/it...)
and it includes a free 128MB USB Thumb drive
i'm assuming you have a monitor, by the fact that your using your laptop through a monitor
and a KB and mouse can be had for $20 or less at newegg
speakers are your choice, but you said you had a headset, so this works in that case
SO
you can get the eMachines, which afaik sports no graphics card, 512MB of RAM, and a 160GB hard drive
or build it yourself, getting an Athlon64 3500, over a 3200, getting 1GB of RAM, almost 100GB more of hard drive space (and it's brand new, i doubt the eMachines would have issues, but this one won't have any (i am personally a Maxtor fan))
and the X600XT is easily fast enough to power through any game you can come up with (At a VERY attractive price)
that is just my suggestion...
here are the product links for the hardware I configured with
if your want to cut costs things to consider cutting:
CPU, downgrade from Athlon64 3500 to Athlon64 3200 (i wish the 3400 still existed for Socket 939)
RAM, downgrade from 1GB (2x512) to 512MB (2x256)
HDD, downgrade from 250GB to 80-200GB sized drive (80's are as cheap as $56, 160's for about $100, this 250 is $135)
Case, downgrade to a $30 case
PSU, downgrade to a Thermaltake or cheaper Antec or Enermax unit
I would not change:
the motherboard
the platform (meaning don't goto Socket 754)
the gfx card (for $124 it is about the best deal your going to find)
the casing (i really wouldn't, it's a great case, and PSU, both from a great company, it includes good cooling (adaptive 120MM fan, should do perfect) and will make things easier)
i would really not change the RAM, as 1GB makes gaming and WindowsXP in general run MUCH smoother
Product links:
Case/PSU
http://www.newegg.com/app/viewProductDesc.asp?description=11-129-159&catalog=23&manufactory=BROWSE
DVD/RW Drive
http://www.newegg.com/app/viewProductDesc.asp?description=27-152-038&catalog=23&manufactory=BROWSE
DVD Drive
http://www.newegg.com/app/viewProductDesc.asp?description=27-151-212&catalog=23&manufactory=BROWSE
Hard Drive
http://www.newegg.com/app/viewProductDesc.asp?description=22-144-327&catalog=23&manufactory=BROWSE
RAM
http://www.newegg.com/app/viewProductDesc.asp?description=20-161-627&catalog=23&manufactory=BROWSE
Motherboard
http://www.newegg.com/app/viewProductDesc.asp?description=13-152-053&catalog=23&manufactory=BROWSE
CPU (includes a HSF)
http://www.newegg.com/app/viewProductDesc.asp?description=19-103-514&catalog=23&manufactory=BROWSE
WindowsXP
http://www.newegg.com/app/viewProductDesc.asp?description=37-102-151&catalog=23&manufactory=BROWSE
Video Card
http://www.newegg.com/app/viewProductDesc.asp?description=14-123-140&catalog=23&manufactory=BROWSE
personally i'd use those parts
if you decide to build on your own, i'd avoid the following parts:
Intel entirely - too expensive for comparable performance to AMD (Currently)
AGP for mid-range gfx - the mobo may be cheaper, BUT the gfx cards will be $100-$150, and that X600XT will probably outperform them all
Bad PSU's - if it looks cheap, avoid it, you want 24A on the +12v or better (or 2 +12v, like the Antec I linked, which has 2 +12v @ 18A each, meaning VERY good power)