You first have to decide on whether you want to build a 386SX or 386DX.
The former is much slower and most CPU's were soldered to the motherboard (no upgrade path) and rarely had cache memory on the motherboard. The latter also came (in some cases) with soldered CPU's but, many also had PGA sockets in order to upgrade the CPU and cache memory on the motherboard
If you want to go for a 386 DX, then I would recommend one that has a PGA socket, 66 MHz or 80 MHz crystal and preferably one that is also "Cyrix 486DLC" compatible in the system BIOS.
If memory serves, none of the 386 BIOSes supported any hard drives larger than 528 MB (or 504 MiB) - I'm now referring to IDE drives. If you want larger hard drive support, then just go the "XT-IDE BIOS on a NIC (LAN) card" route.
Many of the later 386DX motherboards supported much more than 16 MB of RAM, which is more than sufficient for a 386 running DOS and Windows 3.1x.
I would go for a fast 16-bit ISA graphics card (Tseng Labs ET4000 or equivalent).
Sound Blaster Pro (or compatible) is a nice fit for this type of PC.