The IDE connector required is a 44 pin one, like what is found on Kingspec SSD's listed below
These are the SSD's that are a direct plug in replacement for the ATV1:
Kingspec 1.8" IDE PATA 128GB SSD for IBM X40 X41 X41T
Kingspec 1.8" IDE PATA 64GB SSD for IBM X40 X41 X41T
64GB KingSpec 2.5-inch PATA/IDE SSD Solid State Disk (MLC Flash) SM2236 Controller.
128GB KingSpec 2.5-inch PATA/IDE SSD Solid State Disk (MLC Flash) SM2236 Controller
Make that the notch in the middle of the IDE Connector is aligned the correct way up to the gap in the pins on the IDE connector on the SSD.
Your second option is the Micro SATA Cables - mSATA SSD to 44 Pin IDE Adapter as 2.5 Inch IDE HDD 5 Volt
You may get a marginal speed increase over the HDD as the ATV HDD interface can support ATA-100 which has a Max transfer speed of 100 MB/s. Access time may improve marginally.
Currently I get 62MB/s from my ATV / Samsung HDD during testing running Crystalbuntu.
If you have Crystalbuntu running on your ATV1, upgrade to Kodi 14.1 or Kodi 15.0 aka Isengard. This will give you a better Kodi speed boost than upgrading the HDD. Details here:
http://forum.osmc.tv/showthread.php?tid=16811