I have gone to Gili all the forms of transport you mentioned. I have taken the fastboat a few times to the Gili Islands, I have taken the large public ferry direct to Lombok and I have flown from Bali to Lombok
If you are not in the rush take the big public ferry. These boats are huge so I felt safe on them. It takes a few hours to cross but you can get food and drinks onboard.
The fastboats can be hit and miss. One trip we did I was scared. The sea conditions were not good and the boat got tosssed about and waves were crashing over the boat and in through the windows. If the sea conditions are calm then the fast boats are fine.
Flying is the easiest option but it doesn’t save you that much time. You have to check in early at Bali airport. The flight is only about 50 minutes but the airport is in the middle of Lombok so would take an extra 1 hour by car from the airport up to Senggigi Beach.