Starting at Fort William
It is a lot easier and also quicker to start your walk from Inverness but personally after a few days/week away walking, I much prefer to reach my destination and get home as quickly and easy as possible, not hang around towns and train stations waiting for connecting trains. Also bear in mind that the train from Fort William takes 3hrs 42mins and stops at 14 train stations along the way whereas the train from Inverness takes just over 3 hours and stops at less stations. I just want to get home, not be sat in a train. On the other hand, if you travel back while it is still daylight, the scenery on the train from Fort William is fantastic. here's my thoughts on getting to the start.
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 Great Glen Way straight away unless you have planned to end the first days walk at Gairlochy/Spean Bridge. You would be better to spend the night in Fort William and start your walk the next morning. 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.
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 Inverness a few days later, you will have to get the bus 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 bus 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.
Starting from Inverness
As I said, it's easier to get to Inverness than it is to get to Fort William and more places to stay the night before your walk if you choose. There are more shops in Inverness, takeaways and pubs to entertain you or pick up a few things for the walk, if you prefer to stay the night in Inverness before starting your walk the next day.
By Train
You can leave Glasgow or Edinburgh on trains between 6am and 7am and get to Inverness at 10:30am which gives you the option to start your first days walk straight from the train station but you could only really do this if you were doing your walk in the summer when it gets dark later at night as your first days walking would most likely be 20 miles as there isn't really anywhere to stay between Inverness and Drumnadrochit. There are more trains during the day if you prefer to spend the night in Inverness and start your walk the next morning, with the whole day ahead of you.
By Bus
Scottish Citylink run about 8 busses from Glasgow and Edinburgh (changing at Perth) during the day to Inverness, more busses than they run to Fort William. The busses travel along the A9, stopping off at some towns and villages e.g. Aviemore along a very scenic part of Scotland.
By Car
If you travel by car to Inverness, there are long stay car parks which I feel are more secure than Fort William but bear in mind that you would have to travel back here from Fort William after your days walk and you would have a couple of busses after 6pm that go to Inverness so you would have to keep an eye on your time if you are having a long day walking. I would always recommend that you travel by public transport so that when you finish, you can travel in comfort and take in the scenery, text your friends, go online or generally just relax and think about the walk that you have just completed and feel good about your achievement.