First day driving and needing help.

Hey all. Got my permit last week and today they started us off driving on county and city roads with some traffic. I am having problems with takeoffs to the extent I braked early and stopped 12 feet away from a stop sign and couldn't find the courage to get to it without feeling like I might possibly go past it. The breaking feels weird as it is due to never having driven a manual, but I think I will learn to adjust to the sensitivity of the clutch and brake pedals and putting it together. What I don't get is how to smoothly takeoff or inch forward if I have to. I was told to release parking brake with clutch pressed all the way into the break position, foot on service break too, and engine in neutral so I do that. But then when I'm told to slowly let go of the clutch(after placing truck in 3rd gear) and when I feel the vehicle tugging to let go of the service break and keep easing off the clutch until it starts rolling(they want us to start or 3rd gear) I tend to get a slight lurch and honestly it tends to make me nervous. Got so nervous when I stopped at the stop sign I asked the instructor if he could drive it the remainder of the way because I didn't feel like I could safely pull up to the stop sign and do my first 90° right turn into a semi busy road. I've googled this and most of the responses always say to let go of the clutch slowly but they never mention the brakes, when to lift them or anything like that so I was wondering if maybe I'm supposed to let go of the breaks before starting to slowly release the clutch or if the way my instructor told me is the only way?

Edit: actually having just written this I remember the truck rolling back when I once let go of the breaks too early. But are there any tips any of you got to taking off on 3rd gear slowly without lurching at all? Also if it's clutch before break pedal or vice versa for breaking or both at the same time? When I was driving today I always hit the brake pedal first and slowly press the clutch down to slow down to a stop but not entirely sure if that's the correct way.

 

Thank you. My biggest fear is stalling the engine like I did the first 2 times I tried taking off because I slowly fully released the clutch and never let go of the break pedal. I don't think I ever felt the engine pulling before due to that fear so I'd let go of the breaks too early. Thanks for explaining the breaking process. I was doing it this way except for waiting for the rpms to go down. Still felt like it took too long to break for me, maybe I was pressing the clutch in too slowly as I was squeezing the life out of that break pedal.