Is the Godox AD400 a good strobe to use for school portraits? I am leaning towards this unit since it has a modeling light that can further assist with my focus. What other factors should I consider when looking for a reasonably-priced strobe for studio use?
The AD400 could be a good unit for what you need. It mostly depends on how you see yourself doing school portraits, and whether they're single-person or group, shoot indoors or outside, and in what style.
Factors to consider when purchasing a studio strobe would include:
The main reason you go to a studio strobe is for more light, with a bigger spread. The spec to look at for this is the power used by the light Watt-seconds (Ws). Keep in mind, however, that this is not a direct measurement of the light output, but of the energy consumed. Different bulbs have different efficiencies, so comparing Ws to Ws may not exactly be comparing apples to apples. But it's all we've got.
With studio strobes, 300 Ws in the low end, 600Ws or so is the high midrange, with >800 Ws being high output. Typically, expense increases with power output. For comparison, a speedlight is roughly guesstimated to be in the 70 Ws range, but the fresnel head vs. a bare bulb makes such comparisons fuzzier.
Don't just look at the high end of the power, either. Consider the low end, as well, and how much power range the strobe offers. Very low cost lights may only have a four-stop range of 1 to 1/16. Higher-end strobes may have an 8-stop range of 1 to 1/256. Remember, a very powerful light, if it only goes down to 1/16 power, may be too bright for, say, table top or product usage, and you might need to slap an ND gel on it to tone it down.
Monolight vs. Pack & Heads
Some studio lights integrate the power with the bulb into a single unit (monolight), some cable the lamp portion of the light to a power pack, which may or may not drive multiple lamps (pack and heads). Which is more useful to you depends upon your usage scenario. The head in a pack and head system can be lighter and easier to use on a boom arm. The pack in a pack and head system may be more powerful and give a fast recycle time. But the cabling can limit light placement options, and lighting ratios between individual heads. And if your pack goes bad, all your lights are bad. (See also this Paul C. Buff link).
Some monolights today may also sort of give you an option of an extension head for making boom arm use easier by separating the bulb from the power unit.
Another reason to get a more powerful light is so you can use it at lower light levels for a faster recycle than a smaller light. The spec to check here is the time required for a full-power recycle. This will be the slowest the light will be between firing.
Voltage-controlled vs. IGBT
How the flash pulse is cut off can be either through variable voltage control or with some newer lights, an insulated-gate bipolar transistor (IGBT). The difference is in the shape of the pulse. Voltage-controlled tends to have a tail, while IGBT gives a sharp cut-off, and there are resultant differences in pulse duration. Generally speaking, if you plan on using flash to "freeze motion", an IGBT strobe will be better at it. And how you deal with shutter speeds above sync speed will be different between the two technologies.
See also: the Strobist on T.1 and T.5 times.
Reliability / Factory Service / Rentability
Sure, Godox is affordable and widely recommended, but have you tried contacting their support in Shenzhen, China? Maybe you're a professional who needs absolutely rock-solid reliability, super-heavy use, and are a frequent renter when doing out-of-town gigs to avoid hauling your own stuff with you on long flights. Maybe you just want to know you can get a light repaired, rather than replaced. There may still be reasons to go Profoto or Broncolor, or Elinchrom. Maybe you don't want to be sourcing parts from the web, but the manufacturer directly.
How you attach a modifier changes with some different brands of light. You will want to know what mount your light takes so you can figure out if you can use any existing modifiers, you can afford its native modifiers, or if you need to get adapters.
Obviously, the size and weight of the unit need to be considered both for what type of support/light stands you'll need, but also in terms of portability. You also need to assess whether having a light that's capable of being battery-powered or has a battery option built-in is worth it. Typically, AC-powered strobes will cost less than battery-powered ones. Some strobes have an option of being powered directly by either AC or DC power. But most AC strobes do not and would require an AC-output cable battery pack to be used on location away from outlets.
Here are additional features you might want to consider:
Autodumping. When you adjust the power on a voltage-controlled strobe, there may be more stored charge in the capacitor than is needed for the flash pulse, that needs to be discharged before the desired light level is reached. Many voltage-controlled studio strobes can automatically release that charge before taking the shot. Many (such as most AC-powered strobes by Godox) cannot.
Modeling Lights. Output and type are the most common things to be concerned with here. LEDs may not be replaceable if they go bad. Easily-source replacement bulbs, and the brightness of the modeling lights are key. Modeling lights are mostly used to see where the main light will go, but may not be sufficiently bright or cool in operation for sustained video usage.
TTL, HSS. While most models of studio strobes are manual-only, there are becoming more and more strobes that can do some speedlight functions, such as TTL and HSS. If you want these features, you should check that the light is capable of them. Some may only do HSS. Some may do both.
Triggering and Remote Control. Many models of strobes today also come with built-in radio triggering. Check for compatibility (what triggers/lights are in the system). If you've worked with Strobist setups, consider if there's a way to integrate your speedlights. Do you get TTL, HSS, and remote control over power, group, and the modeling light? And if there's TTL, do you get TTL locking in the triggering system? See also: What should I look for in a wireless flash trigger for a home studio?