Acceleration is not instantaneous, it takes a little bit to build up speed. Your throttle indicator is just to the right of your radar, where you have a blue strip next to it. The blue area is where you would have optimal turn control. By default W and S key increases and decreases the throttle. Keep an eye on the throttle and you should see where you're at, and the bar that follows your setting is your current speed. Note that, as mentioned before, your speed need to take a little time to catch up to your settings.
By default the mouse control is set to pitch (rotate up and down) and to roll (spin along your view axis). Some people are not used to the roll when you move your mouse left and right. You can change your mouse X axis to YAW instead in Options -> Controls. Some people feel that's more intuitive as it moves the view like you would a desktop pointer. Note that yaw is generally slower on all ships, so this setting will reduce your performance. And if you remap the mouse X axis to yaw, make sure you map something else to roll. You will want to roll at some point, so make sure you don't end up with no key bindings for rolling.
I would highly recommend playing with your control settings in the first tutorial until it feels right for you.