If the 5150 motherboard is the earlier 16KB-64KB type, the BIOS chip needs to be ugraded, if not done already, to the third revision one. Otherwise the hard disk controller will not work. If it has been upgraded, the IBM part number of "1501476" will be found on the chip in socket U33.
As for acquiring an 8-bit MFM (ST506/ST412 interface) controller, if you want to use the full capacity of the ST-251 (820 cylinders, 8 heads, 17 SPT), then not any controller will do - you'll need one that can deal with a drive of 820 cylinders / 8 heads / 17 SPT.
Alternately, certain other controllers will work, but only partially use the capacity of the ST-251. For example, at
http://www.minuszerodegrees.net/ibm_xebec/ibm_xebec.htm are shown the various controllers that IBM supplied in the 5160. If you used variation #1 or #2, only 10MB (300 of the 820 cylinders, 4 of the 8 heads) will be used. If you used variation #3, only 20MB (615 of the 820 cylinders, 4 of the 8 heads) will be used.