Software would be CX-Programmer.
C200H requires a host link unit.
There are two types, one would go into an open IO slot.
The other mounts to the 40 pin connector on the front of the CPU.
Host link units are no longer available from Omron.
You will need to look on ebay.
I'm sure you can use the older syswin software on the 200H.
I cannot remember the cable but I do remember it was just a 232 to some weird connector, never opened it but it seemed too small to have any converter on it.
I seem to remember a host link that fitted on the CPU 3G2A6-LK201E
but I thought this was for the C20-500 plc's.
Seem to remember there was a cable called C200H CN222
Yes, Syswin will work on the C200H.
3G2A6-LK201 is the CPU mount host link.
C200H-LK201 is the rack mount host link.
Cable for either is a standard null modem cable.
Semi-universal cable diagram is attached.
Pay attention to the Host Link unit you get. It comes in RS232C (DB25) and RS422 (DE9). Both will work on the PLC but you'll need the appropriate hardware on the PC side.
I noticed you have a module next to the CPU. You'll either need to remove the connectors on the module or use a stand off adapter for the Host Link Unit to mount flush. Part number is BP001 or BP002, Pro-Con Base.