In our first travels, we would be taking the hotel car that would pick us up from the airport. It was expensive but we had to spend because we didn't want to get lost. But on the subsequent travels, we had learned how to take the bus or the train by preparing the information of the transportation before leaving for abroad. It is so much cheaper if you travel by train or bus instead of taxi or hotel car.
I usually consider where I am, because depending on the violence historic of the place I always get a taxi. Usually the value is more expensive, but always worth it for the sake of security.
We never take buses, taxis or train from the airport because it would be very expensive especially when getting taxis from the airport. They will charge you a huge amount of money that clearly aren't reasonable. Whenever we travel, we always book a private car or van to pick us up or ask a friend or a relative if there's one near the place. That way we can save a lot rather than using public transportation.
This really depends on where you are going. Cities are well serviced with trains, and buses but remote areas or places that are put of season won't have these services. I usually always take a bus or train, but if it's late I will get a cab because it's safer. Plus if you have a few passengers and lots of luggage, public transport isn't worth it.
I don't think this is a good idea. Well, no offense, but doing it seems silly. I mean, I tried that once in South Korea and was made fun (on the subway). Well, I didn't exactly try what the OP is saying. What I did was an attempt to bring my huge bag from an area of Seoul to the airport via a subway.
I generally take Metro Train back to bus stand while on my way back to my home city which is almost 100 km away from my home but I have no choice but to book a taxi for airport if I have more than 2 pieces of luggage with us. Incidentally there is no airport in my city of residence but about 90 km. I generally find a car waiting for me either by my company or by the hotel where I am supposed to stay.
I always try to take the metro/train or bus because they are way chepear and I can use that time to get a glimpse of the city where I´m at. One thing that helps me is that I always travel light or try to at least, so I can easily board the bus or enter the train without making anyone unconfortable. Unless it is really late or early in the morning and I feel the area is a bit insecure or so, I can sometimes take a taxi.
I try always a cheaper way to reach a destination. I can save money through this and the best way also to have a memorable time.