The best way to get to and from SML is the Nantou Bus company from the Taichung HSR station Exit 5. It takes about ninety minutes and costs about NT$200. Here is the schedule. Sorry it is all in Chinese. Incredibly, this information does not seem to be available in English. I guess this is still Taiwan. Anyway the buses are hourly at eight minutes past the hour. Just start asking when you get to the HSR stations. Middle-class Taiwanese people love helping foreigners. You need a little patience. You will get there.
Once you are at SML, there appears to be an bus service around the lake. Here is the schedule. Again. none of this seems to readily accessible in English. There is an NT$80 day pass that might be useful.
As for true packages, EZ Travel has some for NT$3,200 or so. Call them. I’m sure they have someone who speaks enough English to help.
You have enough questions that you should really just buy the LP book.
And SML sucks!