Is everyone trying to upgade with UA miles these days?...During the last 1-2 days there has been 3-4 inquiries on upgrading TK flights with UA miles.
To answer your Q: When you make the reservation online (website or app) the booking class will be stated when you select flights for a specifik travel date. S, H, A and M are fare classes in the higher end of Economy so if you are searching for dates will cheap fares available, you will most likely not see one of these fares.
Note of caution: As it will be apparent from the other posts during the last days about upgrading TK flights with UA miles, you also need I class to be available in order to upgrade, i.e. in add. to purchasing a quite expensive economy fare you also need TK promotional award availability (similar to UA saver award) to be present, which for US flights is almost impossible to find (TK do not release many award seats on its US flights and they are in high demand by pax looking for award tickets) You will see that this comes as a surprise to the other posters. Unfortunately, to upgrade is not only a questions of booking a TK ticket in right booking class.