Inverters as a whole are usually constructed as cheaply as possible. Even the nice Black & Decker ones you pay out the nose for really are pretty shoddy. Because of that, I usually recommend people buy an inverter with a sustained power rating (NOT SURGE!) around 50% more than they expect to use on a day to day basis.
This will make sure it doesn't go nuclear on the first blistering hot day when you dive into the car and turn the inverter on without letting it cool down.
The power supplies you'll be plugging in should all have a maximum wattage, or at least the max input voltage and current (simple math). Add up all of the power supplies you expect will be plugged in on an average chase, and multiply that by 1.5.
One other thing to consider is the fact that the cigarette lighter plugs in almost all vehicles max out at 10A (120w). Its a bad idea to run anything beyond a single laptop power supply (and sometimes not even those depending on the size of the laptop!) off of these outlets. When they blow the fuse, they sometimes take unexpected equipment like A/C fans or interior lights with them. That sucks in the middle of a chase, trust me. Inverters really should be hard wired to the battery through a properly selected fuse. If you're absolutely stuck with the cigarette lighter, I'd stay around 300w, and test all your equipment on the inverter BEFORE chasing.