From a whitebox standpoint, the hardware 'should' work:
http://www.vm-help.com/forum/viewtopic.php?f=13&t=2484
Thing is, this individual tested with ESXi 4.1. I would recommend try to get your hardware to work prior to investing in ANYTHING additional. You may be able to load ESXi 6.1, you may not. If you can, then you may want to invest in additional resources...
From what I have read on the T7400, it could work. You may need RAM, and it appears this would work:
http://www.amazon.com/Memory-Precis...449504745&sr=8-1&keywords=precision+t7400+ram
The above is very cheap for 16GB, but I would suspect it may be one of your best bets.
I'd recommend throwing an SSD or two in there if you don't use RAID. As disk is shared, spinning SATA disks are going to be slow (and can be unbearably so at times). If you do use RAID, you could potentially do ok with a RAID10 on some spinning disk, especially if you want capacity (file server).
As for the recommendations above... they're good if you're trying to build a production home box of sorts, but if you're just figuring out the nuts and bolts, you don't need to over complicate it. Just make sure the MB has been tested and validated by someone. And honestly, for most builds, just about anything works. You simply need:
A supported Gigabit NIC (Intel are readily available:
http://www.amazon.com/Intel-Gigabit...&qid=1449505366&sr=8-1&keywords=intel+gigabit). You can download MIBs and inject them into a disk or add them to your host to support other NICs (Realtek for instance)
A supported disk. Standard disk controllers work, or real RAID controllers (this could work:
http://www.amazon.com/HP-462919-001...d=1449505468&sr=1-12&keywords=raid+controller). You do not typically want to use a consumer grade type of RAID controller that is built into the board as they are most likely not supported. As to disk, SSD is your best best for performance. Just need to be aware of how big of VMs you plan to build. As this is not a production array/build, Thin provisioning will save you some disk space.
Beyond those two things, you can typically get an install to work fine with just about anything. My home box is running an unlocked Phenom X3->x4 on a 760/780 chipset (can't remember which). I have an Intel NIC and a Realtek NIC (unused, but the MIB is loaded). And I have a RAID 5 of spinning 250GB disks, and 2 x 2.0TB and 1 x 3.0TB for the MythTV DVR. The ESXi load is solid, the build is stable. No complaints. For your testing you don't really need to invest much of anything other than in disk and maybe some more memory. As long as your platform suits yours needs, use it. If you decide to try to get more out of it, then invest if you aren't able to get enough out of your current platform.