OK this will be the most basic of introductions. I was a nuclear electronics technician in the navy for the best part of a decade, and have also done micrometeorology as part of my forestry duties, so I have quite a bit of experience in atmospheric measurements.
First, you can actually find mercury or alcohol thermometers that have a little bead in the tube that sticks a little at high temp and you have to shake it down to reset it. That'll probably be the cheapest or at least easiest to use. There are also bimetal strip units that have a dial that sweeps to indicate temperature. I've seen them with limit bars that are reset by twisting them back to a nominal zero.
Then there are electronic devices. There are three basic types -- thermocouples, resistance temperature detectors, and thermistors. These measure temperature quite differently. Using a thermocouple, you are measuring a change in voltage proportional to a change in temperature. RTD's are the exact opposite: you measure a change in resistance proportional to a change in temperature. Thermistors are also resistance devices, but they work through different means.
All of these electronic devices need to be plugged into something that can read and display the temperature as measured. A cheap device will have the detector integrated into the display; an example of this would be a digital oral thermometer. Better devices allow you to configure detector and display as needed.
Here's where the "what do you want to do with the data" part comes in. If you want it to output in some sort of useful digital form, like a table that can be inputted into a spreadsheet, you'll pay more. If you are happy to take notes by hand, a glass or bimetal unit will do. As for prices, I'd start by searching Amazon. You can pay anywhere from pennies to thousands of dollars depending on features.
