Personally, I suggest going directly to Lingyin Temple, because there is a bus stop there, and it is very convenient to go to the West Lake (it is difficult to take a taxi in the scenic spot! )
If you only have one day, I think you can go to Lingyin Temple in the afternoon (it has opening and closing time) and sit by the West Lake in the evening. In fact, it is best to find a place to sit quietly and watch the West Lake.
The day is only half a day. If you want to visit more scenic spots, you can choose to rent a bicycle to walk along the river (the scenic spots are all blocked), so you can basically visit many scenic spots, such as Broken Bridge and Su Causeway, which are all around the lake. It's ok to take a boat at the dock, just like the boat in Hangzhou. On a pier, you will go to the island in the middle of the lake and then go to different places on the island. You can't go back. If you want to go to another scenic spot by the lake, you have to spend money to shoot it again before you go to other scenic spots:)
By the way, there is also the kind of sightseeing bus in the scenic spot, which is also very convenient and can be seen everywhere.
Because you are too pressed for time and want to visit many scenic spots, you'd better recommend cycling or sightseeing bus. In the past, when I went with my family, I went to one or two scenic spots by boat, and it was gone after a little stroll for half a day.
Also, there is no subway in Hangzhou at present, so it is blocked on weekends. Pay attention to the time.