Inverter grounding

In theory, you should attach the chassis ground screw/stud of the AC inverter to the DC Return (usually Negative terminal) the battery negative bus (either the same diameter of your +/- cables, or at least #6 copper cable). If there is, for example, a short between the positive DC bus (internally in the inverter), and the chassis of the inverter, this will pop the positive DC fuse/breaker from the positive battery bus.

And run a ground wire (for your 2000 watt inverter, ~17 amps max output) 12 AWG cable from the "common" battery return ground bond (negative bus typically) to the green wire grounding of your AC system (at the home's ground rod, cold water pipe, etc.). This is to make sure that any AC hot to ground short (appliances, AC wiring, etc.) shorts will safely short the AC inverter and shut it down rather than shock somebody.

Note, smaller PSW/TSW AC inverters typically "float" The AC neutral/white wire. Larger inverters (and generators) typically Neutral/white wire to Ground (chassis) bond (or generator chassis bond).

In either case (floating AC Neutral or Ground Bonded Neutral) are safe when using GFI outputs. Note that any Neutral/Ground bonding  is "before" the GFI breaker/outlet inlet. If you Ground Bond the Neutral on the output of a GFI breaker or outlet, it can/will pop the GFI protection (especially if you have 2 or more Neutral/Ground bonds).

And if you have a MSW type AC inverter, you cannot do an AC Neutral/Ground bond on the AC output (and the ground bond the DC negative bus)--This will "short out" the AC inverter internal transistors.

In general, Ground Bonding to a Ground Rod/cold water pipe is for Lightning protection (and static discharge, reduce chances of corrosion, etc.).

Ground bonding the AC neutral, AC chassis/green wire grounds (and DC negative ground to inverter chassis ground/epanel chassis grounds, etc.) are to ensure that any "Hot" to chassis short circuits will pop protective breakers/fuses (or electronic protection on AC inverter outputs). You don't want, for example, a sink to be "hot" with DC or AC power.

There are other reasons for "ground bonding" (such as easier starting for flourescent lamps, flame detection on automatic spark natural gas/propane igniters)--But those rarely apply to solar power system these days (LED lamps, etc.).

-Bill

As I understand, a grounded three prong socket (with neutral/ground bond) is "per code" as safe as a ground bonded neutral, no green wire to ground plug, behind a GFI Breaker or outlet (in old homes, without a ground wire to the outlet, a GFI outlet or breaker is an acceptable upgrade vs having to run a greenwire to all outlets.

Your small inverter probably does not have a Neutral/Ground (to inverter chassis ground) bond internally. It is, probably, a floating AC output. That plus a GFI outlet on the inverter is "safe".

With floating AC outputs, wiring and safety issues get a bit "complicated". Floating AC outputs (such as behind an isolation transformer) are "touch safe" (if you touch one wire, you cannot get a shock because you do not complete a circuit). However, if there is a short from one AC line to metal/ground/etc., it is no longer floating and can become a shock hazard (isolated supplies are used in manufacturing to test equipment being built, but before final Hipot testing for safety). For these systems, there is a required (monthly?) test that the outputs are still floating (no internal shorts) because a "shorted floating output" does not automatically turn of the AC power (no tripped breaker, etc.). The GFI does still protect against you touching a "hot wire" and ground by shutting off the power (obviously, if you touch the Black and White 120 VAC wiring, you will get a shock, GFI devices do not protect against these "faults").

But from your point of view, as long as the wiring is done correctly (right size and type of wire, proper terminations, wall outlet mounted in box, no exposed "hot" components, etc.)., your AC output protected GFI outlet(s) is(are) going to be fine. And you should not have any problems with appliances plugged into the outlet.

-Bill

How about asking the question backwards... What kinds of loads do you want to run? Will the Solar Outlet be near any sinks/water/etc.?

More or less... Assuming just a home office and "normal office loads", I would run a 6 AWG cable from the inverter chassis ground to the battery negative bus (negative ground bus). And I would run a 12 AWG or heavier wire from the battery negative bus to a ground connection connection at your main panel, house ground rod, cold water pipe, etc. And call it a day.

Run 3 prong sockets (Hot, Neutral, safety Ground) as normal in the office, don't bother connecting the safety ground. This is assuming your 120 VAC solar power is from (after) the GFI outlets (GFI protected).

More words/explanations, does not change the above suggested wiring. Read at own risk...

The 6 AWG wire from chassis to battery negative will "short out" any +12 volt to inverter chassis shorts (wiring, transistor cases, etc.).

The 6 AWG chassis to battery negative to 12 AWG or heavier cable to the "house ground" will protect against any normal 120 VAC short circuits and other house branch circuits/etc. shorted to your solar 120 VAC (i.e., a computer connected to solar, and a  120 VAC utility power laser printer networked through USB or something--And there is a 120 VAC short). Either the solar GFI or a 120 VAC circuit breaker (house or solar) will trip (and keep things safe).

You could run a 14 AWG cable from House ground (somewhere) to 120 VAC solar outlet ground green screw--But not really needed (leave outlet ground socket floating).

And you should keep your Black (Hot) and White (Neutral) wire from the inverter to the office outlets properly connected (polarity--The ground bonded neutral/white wire from inverter to socket white screw). Reversing Hot and Neutral at the outlet is not considered "kosher" under NEC). It is assumed that (at a minimum) power switches are in the "hot leg", the threaded portions of light bulbs are "neutral", etc. (for examples).

The reasons for having "code" and following "code" is that 1) everyone "knows" the wiring rules and 2) much of the reason for code is to catch the "weird" failures (short circuits 'anywhere', water intrusion, rodents eating wiring, etc.) and to reduce the chances of fire/shock.

And, if you live in a lightning prone area, connecting the grounds between the House and Solar power systems will help keep "all 120 VAC circuits" at the "same voltage" (don't get an arc from solar AC to utility AC).

-Bill