Oh definitely InshAllah, it all happens slowly with time..But you also know that such is the awesomeness of Allah swt's guidance that sometimes some of the most staunchest enemies of Islam have reverted to it, so you never know. I would like to know one thing though, would your parents be bound by their belief to cut you off, or if, god forbid they decide to cut you off, it will be just their personal decision? I doubt though that they'll be able to cut you off for long, since you'll be a really nice kid from now on for sometime, and buy them their favorite stuff or etc

and they're bound to notice the change in you, who knows they ask you themselves what inspired you..you can just say you're inspired by Islam, and it surprises yourself too... hehe.. Dont take it too seriously, you can think of a thousand ways to go about it, May Allah swt help you choose the best one...but in any worse case scenario, you can ask for their support before you declare your conversion... something like, that you will really appreciate it and it would mean a lot to you if they just didn't show any angst against what's new going on in your life and it would really help you if they tried to understand it, and the fact that your change of faith will not have you take you far from your parents and you will be taking care of them whenever required. ( i guess thats not done much in a western society but in Islam its kids who are supposed to take care of parents, not old homes, anyhow thats a different topic).
But I agree very much with your thinking that first you have to settle in well a bit in islam before you make that declaration to them, you must be prepared for opposition and questions, as well as you must have developed some strength by that time which will ease up your anxiousness InshAllah, dont worry at all. For Allah swt says in the Quran that those who believe in the One God and the day of judgment will not be depressed nor shall they find any grieve in here and the here after. Ignore your whims of darkness/sadness as tricks of satan, he gets really happy when we get depressed and hopeless from the Creator, that is his main goal.
Say Allahu-Akbar loud when you get any sad thoughts, and also the first kalima , satan runs far from it. Best to you Ameen
p.s i can tell you more zikrs ( words, verses) later, which when said before a conversation, not only help you say things in the best manner, they also affect the hearts of the listeners and help avoid arguments or rudeness.