You can download and read the USBTMC standard, and eventually figure out what it means. There are also a lot of open source USBTMC drivers that you can refer to, such as the linux kernel driver and the python-usbtmc userspace driver. You used to be able to find the USBTMC definition on usb.org, but it seems to have been reorganized for maximum confusion since I last visited. Here is a copy someone posted:
http://sdpha2.ucsd.edu/Lab_Equip_Manuals/USBTMC_1_00.pdfWhen you say "set the measurement range, start a measurement, read the result" -- those are higher level concepts than USBTMC, and are about sending device specific SCPI commands. USBTMC is concerned with sending messages, receiving responses, and executing control commands such as clearing the interface or aborting an in-progress transfer. USB488.2 includes equivalent behavior to IEEE 488.2 such as serial poll and SRQ to notify you of events such as a measurement completion but that is still lower level than the application level commands you are talking about.
My suggestion is definitely to get things working on a PC first using libusb. Most of the higher level code should stay the same if you want to move to a microcontroller, you will just have to replace the libusb calls with your appropriate platform USB calls.