When should I start preparing? Count back from the deadline
Work backwards from the deadline. For an early-December deadline, the credential evaluation has to be moving by late September if you are using WES, letters get asked for by early November, and TOEFL or GRE should be done by September.
Each of those has its own wait: the evaluation takes 6–10 weeks end to end through WES or 3–5 through ECE, longer in peak season, letters need four to six weeks' notice, and score reports take one to two weeks. There is one more stretch after decisions come in, because the I-20 only exists once you are admitted and the visa interview waits on the I-20, so the three months after spring decisions are for the SEVIS fee, the DS-160 and the AIT appointment; the official advice is to start the visa at least three months before you plan to leave Taiwan. How long each step takes is written up in its own entry. This one only puts them in order.