Since it's gas, you need to follow the code-required minimum square footage (inches) for air flow for combustion.

In addition, make sure to make he closet big enough for you (or new home owners) to be able to "easily" get in there to service and/or replace it down the road.

 

I have a similar looking unit and all the ventilation/clearance requirements are printed on a big sticker directly on the unit... Maybe check around back of it? Or find the model online. All will be explicitly stated.

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I think if you build a closet wide enough for a 30 " door and the door slab is 6" away from the tank.
And you have a vent in the door or wall for fire air.
Unless it is in a bedroom or bathroom then it is a sealed door with air from outside.

Can you install a gas water heater in a closet? (howtolookatahouse.com)

 

In my neck of the woods a gas water heater has to be 18"above the finished floor.

Something about vapors from flammable liquids.

I replaced my water heater and although it was not required by code when my house was built, I raised it the 18" just in case.

Mine was in a garage, your's may be different.

What are the code requirements for the pressure relief valve piping..

Here the relief piping has to empty outside.

I'm not running a 3/4" pipe across my garage floor.

 

I think it's about 30" room all around. This is so a repairman has the room to work. If you stand two walls there, most likely you will frame a corner post which could block the access/removal. I would finish the room as you want then cover it with panel walls that are easy enough to remove. Panels should be as fire resistant as possible. Make the panels with metal studs and line the inside and outside with metal louvers. Louvers for air. That is a must. Not sure so verify, I think the ceiling and the part that is on top of the foundation (joist bays, rim joist, etc) need to be fire resistant too.

 

Thought of this too late for edit. Gas appliance must have make up air. Sorry, I don't know anything about it. I asked about it before and still don't get it. It's got to do with oxygen for people too. If you're framing for a room, you may have to add outside air intake.

 

This is a direct vent unit. Does that change any of the rules ?