By all means build a computer for him.
Skimp on:
Case
peripherals
video (use onboard)
sound (use onboard)
Buy decent: better than average, but don't go cutting edge...costs too much
RAM - 3GB unless you use 64 bit OS and apps, otherise go 4 or 8
motherboard
processor
Spend extra on:
Hard Drives
Fans and Heatsinks
Power Supplies
And have a plan for when hard drive, fan, or power supply fails.
For processor, use a Core 2 Duo, 3GHz or higher. Reason? Simple, save a ton of cash over i7 or quad core. Pack it with RAM, but if you're not using a 64 bit OS, over 3Gigs is a waste.
As for software, sounds like he's running a database based system. Highly recommend looking over at one of the shareware repositories looking for software that does what you need it to do. He cannot possibly be the only veterinarian running a small business who needs "veterinary/medical record keeping + shipping & receiving + payroll" software. Someone has done this before.
Consider 3 or 4 machines. One for the database/file server. One for the front desk where the work is done. This one gets a nice monitor keyboard and mouse. The third is the backup machine. Server and backup machine need to be Raid 5 for redundancy, and the backup machine should be offsite. An online data repository might work for this, depending how much DATA needs to be backed up. Don't backup the OS and apps this way, a ghost type image taken after install+update is the best way to back those things up. This keeps the backups small.