What is the most advanced logic board compatible with my system

James you have the top model of this series of MacBook Pro systems. As such there is little one can do here as far as upgrading the logic board. Each series of systems Apple alters things just enough to make it very hard if not impossible to upgrade the logic board.

With that said there are some things you can do to gain more life out of your system:

• Like upgrading the memory to 3 GB (you can use two 2 GB modules so you gain interleaf, but thee top 1 GB can't be accessed as other system resources are using the memory addresses). Given the price difference you might as well go with 4 GB (2-2GB modules) Vs having a mixed set (1-1GB & 1-2GB modules).
• Upgrading the HD to a hybrid drive which is a HD with SSD caching in one device. The only thing you need to watch out for is the SATA I/O speed of your system is SATA I (1.5 Gb/s) so you will need to make sure you get a unit that can run at this lower I/O speed. In any case make sure you have upgraded the EFI firmware to the lasted this model uses. Here is a link to check it out and update it as needed EFI & SMC firmware updates for Intel-based Macs.