Detecting trash (plastic) burning smoke with sensors
The typical gas sensor marketed to hobbyists and enthusiasts (except for $\ce{CO2}$) are of the metal oxide semiconductor type, not to be confused with MOS as in MOSFET.
How do these work?
In these detectors, a semiconductor material made of the oxide of a metal, usually tin.
I'll quote from this question:

...sintered composite based on the semiconductor material $\ce{SnO2}$, which is the metal oxide. The different sensors have different admixtures and operating conditions to achieve different sensitivities to different gasses.
The principle of operation of MOS-type gas sensors is explained in Figaro sensors' Operating principle; MOS type.

The Figaro link shows the operating principle in the GIF below:
 GIF (Source: Figaro)
When the $\ce{SnO2}$ is heated by the (usually 5V but not always) heater supply, oxygen in the air will dissociate at the surface and oxygen ions will stick to the surface, depleting the semiconductor and cutting off the flow of current. When a carbon-containing gas (e.g. $\ce{CO}$ or $\ce{C_xH_y}$ (but not $\ce{CO2}$)) comes along, it will combine with the adsorbed oxygen and remove it from the surface. The more gas, the lower the equilibrium concentration of adsorbed oxygen and the higher resulting current flow through the semiconductor.
Not as gas-specific as you might think
By adjusting the amount and types of additives to the sintered $\ce{SnO2}$ and adding catalyzing metal clusters to its surface, the manufacturer can enhance sensitivity to some gases and reduce it to others, but there is no single-gas specificity with these sensors.
Since the carbon in $\ce{CO2}$ is already fully oxidized, it won't react with the adsorbed oxygen. Those sensors (e.g. MG-811) use a chemical cell sensor based on a solid electrolyte. They need very high impedance amplifiers that measure millivolts, a bit like pH sensors, in fact, a lot like pO2 sensors!
CO and VOCs
I would recommend you use a $\ce{CO}$ sensor (e.g. MQ-7, MQ-9, MQ-307A or MQ-309A) since burning garbage will likely be incomplete (not in an industrial incinerator) and a &quot;Air Quality&quot; VOC sensor like MQ-135.
You can experiment with others, some people like to build an &quot;electronic nose&quot; which is an array of a bunch of these, then they plot the data for different kinds of smoke and environments to see what happens, and try to use the pattern to identify the likely problem.
PM2.5
Inefficient combustion can also produce particles as soot, and there are more expensive &quot;dust sensors&quot; or &quot;PM2.5 sensors&quot; which measure small particles (2.5 microns or larger) in the air. Soot is a hallmark of incomplete combustion (think of the smoke from a badly tuned engine) and a huge problem from incomplete or low-temperature combustion from a garbage fire.
None of these will be conclusive, you'll have to look at your data and look at when there is a fire, and learn how the signals correlate to the events.
Ultraviolet light
There are UV light based fire detectors as well, but you'd need direct line-of sight access to the flames. If the sensor is designed to be solar-blind by adding a filter that removes all wavelengths from the Sun that make it to the ground, then it might be helpful here. However, they are usually designed to work indoors where indoor lighting may have less UV than outdoor sunlight. This would take some more investigation.
read the data sheets carefully
Finally, read each sensor's data sheet carefully and note carefully the specific voltages that each sensor needs. The &quot;Air quality&quot; sensors need you to run for a certain amount of time (about a minute) at one voltage, then a different amount of time at another voltage because the surface chemistry is a bit more complex.
Sensors can also be found here:

http://wiki.seeed.cc/search.html?q=gas+sensor
https://www.pololu.com/category/83/gas-sensors