You can grow with nothing more than the base nutrients if you like, but the Advanced Nutrients line was designed to be used in its more robust incarnation.
Realistically, I'd say to just get the base nutes and a couple additives (don't miss Big Bud) the first time out. Save a little money, get a little experience, and keep things a little simpler until you're more familiar with the whole process.
The way it works is you put in whatever additives you have at the amounts on the calculator. Then, once that's done, you measure your ppm and then add enough of the base nutrients to bring the solution up to the target ppm.
Where most people run into trouble is trying to do it backwards - mixing nutrients from the base line until you're at full strength and then adding the additives to that.
And it's never a bad idea to start a little light on nutrients and slowly work your way up. It's easier to add more nutrients than it is to take them out.
Don't forget, you don't need to feed the seedlings. Let them grow a couple weeks without food. The first leaves that appear should turn yellow when you need to start light feeding.