What you are saying is correct. However, my understanding is little different. Most of the graduate students are funded my some sort of federal grand such as NSF, NIH, DOE etc. This is not consider their grant, this is their advisor's grant. Working on federally funded project is definitely good point, but I would not emphasize too much on it unless I am one of the PI or Co-PI on those grant. Most of the graduate students or post doc write proposal for their advisor, but if it does not have your name on it, then it is not yours. That is what I understood. 

"F1-OPT-H1-GreenCard, is the general route which most of the people take but it is not the route everyone must  take." My lawyer said to me. 

"F1 can easily transfer to H1, H1 has dual intent, can file green card with no problem, why not F1 directly to Green card, big debate going on among lawyers" I read somewhere in internet. It is all big puzzle for me. Good luck to all of US.