Car has been acting up when first starting for months and slowly getting worse. Now when I first start it, the car will run rough and die if I do not press the gas?

Also, when I put it in reverse especially to back up, it will die if I don't give it
gas. This is only when I first start the car though. When I get to the end of my
driveway coasting without giving it gas, it will die before I get to the end and I
have to mash the brake pedal hard to stop. I start it up again, hit the road and
for the first few feet it acts like it doesn't want to go, but once I get up to speed
it runs perfectly and smooth. Then when I come to a stop sign or light, if I have
to sit for more than 2 minutes it gradually starts to run rough again and dies
and I have to restart it. I'm so baffled because I've thought about several
options like the IAC, DPFE, Mass Air Flow, etc. but I really don't...DON'T have
extra money right now to just throw at the car. I do need it though and this is
really getting annoying. I tried to describe it as best I can so maybe someone
else has had this problem or has a good idea of what it is that sounds more
definite than 500 different "maybes." If anyone out there has a good idea of
what the problem is PLEASE give me your thoughts. I promise I won't judge
anyone who responds, but I'm hoping someone with the Ford 4.6 Liter engine
experience in the past can tell me something. It's gradually gotten worse and
worse and it needs my attention. HELP! Lol