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 Chief is always the highest and probies the lowest, from there it depends on the department, though there are a few "rules."

Captains are higher than Lieutenants.  Some departments have battalion, division, and assistant chiefs, generally in that order.  

Structure resembles military command structure.  In most cases, a lieutenant or captain will be in charge of each piece of apparatus and its crew, with a captain in charge of each station.  Some departments, such as Houston, have junior and senior captains. Several stations will be grouped in a division and several divisions will make up a battalion, though some departments don't have either divisions or battalions.  Assistant chiefs will generally be in charge of administrative functions: training, maintenance, etc.  At the top sits the chief, though a few also have commissioner, which is generally a politically appointed or elected position.

In my department, we don't have lieutenants, only captains, we also don't have either division nor battalion chiefs, only assistant chiefs.

I think all departments use the same basic rank structure. Some departments just don't use all the positions. We have firefighter, lieutenant, captain, battalion chief, assistant chief, and chief.

I don't know about everyone else on this site, but I would actually really appreciate you using actual firefighters for reference. I think I speak for all firefighters when I say that we would appreciate a good firefighter game, and anything we can do to help make it a good one would be a pleasure. Ask away I say...

As for the terminology goes, "boots" is a local term and is not common enough to include, in my opinion. I would stick to the more common terminology like probie or probationary.

Rank structure has absolutely nothing to do with NIMS, which is designed to work across all boundaries and incorporating fire, LEO, EMS, public works, etc.  NIMS' command structure is completely separate from any fire department rank structure, having its own setup.  A chief under NIMS is in charge of a division and is not at the top of the structure, that's where the incident commander is at.

In addition, NIMS specifies that the person placed in any position be the most experienced and/or qualified to fill that spot, regardless of the rank.  So you could have a captain placed higher in the NIMS structure than a chief.

NIMS does mention common terminology within the NIMS command structure, while also specifically mentioning that this has nothing to do with their everyday titles.

The goal of NIMS is to bring together disparate groups from radically different fields with different technology and terminology.  Within a NIMS command structure, you could have LEO, EMS, FD, Public Works, utilities, and private elements, none of which might have the same internal rank structure.

The NIMS command structure is the same regardless of IS-100, IS-200, IS-700, IS-800.A, IS-300, or IS-400.  Those are just different levels of training that you take.  IS-100 and 700 are an introduction to ICS/NIMS, IS-200 applies ICS/NIMS to a single-incident or initial response, and IS-800 introduces you to the National Response Framework (what happens when you call in state and/or federal resources).  IS-300 deals with large scale incidents, including the various meetings and paperwork that needs to be filled out.  I've not taken IS-400, so I can't comment on that course.

We're all familiar with ICS and hopefully use it on EVERY incident.  NIMS takes basic ICS and expands it to include all possible resources that might be needed at a major incident, hence the reason to have common terminology that extends beyond organizational boundaries.  Unfortunately, it seems that only the fire and EMS services have been taking NIMS seriously, which does not portend well for the next major incident.  It's also the reason you see FD personnel almost always be IC at a major incident, because we're the only ones that know what's going on.