Starting at Fort William
There are good and bad points about starting at Fort William, one of the good points is that when you finish the walk at Milngavie, it's a lot easier to get home from. If you finish in Fort William you may have to wait for a train and then sit 4 hours on it until it reaches Glasgow about 10pm, which isn't ideal. Starting the walk fresh in Fort William means ending at Milngavie and getting a train the short journey to the main Glasgow Railway stations and then heading home from there, a lot quicker than finishing in Fort William. The downside is that the best scenery is at the Fort William end of the walk so you feel like you're doing the best days at the beginning and not having the fantastic scenery in front of you as you near Fort William.
By Train
If you are travelling by train to Fort William from Glasgow or Edinburgh, you only have 2 possible trains (at the time of writing) or 1 that reaches Fort William after 10pm. The earliest you will reach Fort William is just after noon so it would be pretty difficult to get off the train at Fort William and start the West Highland Way straight away unless you have planned to end the first days walk at Kinlochleven in the evening at a fast walk. You would be better to spend the night in Fort William and start your walk the next morning, fully relaxed. There is the option of getting to Fort William just before 10am if you get the Sleeper train that starts in London but I don't imagine you would feel very refreshed after arriving at Fort William after a night on a train. In short, if you get the train, stay overnight in Fort William and set off fresh in the morning.
By Bus
Scottish Citylink run bus services from Glasgow to Fort William every 3 hours, the first bus being at 7am which reaches Fort William at 10am. The bus actually takes over 90 minutes less to get to Fort William than the train. Crazy, huh? The Citylink bus from Edinburgh goes through Glasgow on its way to Fort William. The journey isn't as comfy as getting the train or as scenic but is generally cheaper and would let you set off to Kinlochleven when you arrive instead of staying the night in Fort William.
By Car
If you are taking the car, obviously you can make your way to Fort William any time you like and carry more stuff with you. A downside to taking your own car is that when you finish in Milngavie a few days later, you will have to get the bus or train back to Fort William to retrieve your car. There are a couple of long stay car parks in Fort William if you feel comfortable about leaving your car. If you intend staying at a Bed and Breakfast the night before the walk, enquire whether you can leave your car there for the few days, no harm in asking and you'll feel happier. It might suit you better taking the car but do you really want to complete your walk, then get a long bus or train ride back to the start and then set off back home in your car? If you take the car, think about spending a night in Fort William when you get back there to rest then head for home the next day.