I had the exact same intent when I joined the game--my partner and I logged in together and rolled toons at the same time. So there are a few suggestions I can offer beyond repeating what everyone else has already said.
Be aware that there are a number of early missions--including the entire tutorial--that you can only play through solo. We were very confused at first because we weren't showing up in each other's missions even though we'd teamed. Just team up and get through the tutorial missions--as soon as you hit Sector Space (the equivalent of the world map or overworld), the game will try to put you and your teammates in the same instance.
It is not immediately obvious when the tutorial ends and you are completely cut free. I don't wish to spoil anything, so I will simply say that there comes a point in the first handful of missions where (for Fed players) you return to Earth Spacedock at the conclusion of the mission; for Klink and Rom toons it's Qo'noS and the Flotilla. Sync up with your friends and decide where to go from there.
It's totally okay for one of you to level up ahead of the others, or for someone to fall behind. STO has a "mentoring" system that allows you to match the team leader's level. Just make your lowest member the team leader, and try not to be in different zones for too long.
Ignore the haters. Not because they are wrong, because there are a number of very legitimate complaints that can be raised about the game. Ignore them because that's all they have to offer and what they want is to discourage you from playing. So play the game and form your own opinions. If you can't stand some particular feature or bug, that's your call. But your life and playing experience will not be enriched by reading the 214381957392711th thread on why Cryptic just wants your money or is trying to kill the game.