I've had a look at your situation in DOTM and despite you managing to find an airport where no-one is based, it doesn't look like a good choice. It closes at night too, which is never a good move.
There are plenty of large airports with no-one based there. If you look on the airlines on map in this game, some European countries have no airlines based there and the same goes for some US states, the Middle East (Abu Dhabi for example has huge potential) or the Indian sub-continent. If you can start up in one of these, then you can learn things very quickly. There will be plenty of capacity from these airports.
3 million is plenty to start with - you can get a bit more with a loan too. The used market has plenty of great start-up aircraft like DC-9s, 737-100s, 727-100s etc. You can build up a decent fleet using these and then when you have enough money, you can then order new, or keep plucking better aircraft from the used market.
Competing with large airlines is always hard, but you can still make decent profits by undercutting them. If the airport has 2 or 3 large airlines then you can sneak in for a while, as large airlines are extremely difficult to micro-manage. By the time they've realised you're doing ok, you've made some cash and expanded a little, thus keeping you sustainable. Expanding quickly is always key to a successful airline at the start I've found.
I hope that helps a little - most of it you learn through your failures. Fleet commonality and capturing the business class market on routes are my main 2 tips