Hesitation and dying!

When cold, my 78 mustang II ghia (302ci, carburated) will die, which isnt that big of a deal, except that after I warm it up, when I come to a stop the car also occasionally dies. To counter that, I drive it like a manual (I kick it into neutral when I stop, because it usually only dies in Drive). Also, there's a certain spot where I press the accelorator(or if I floor it) that it'll badly hesitate before kicking in, and if it's semi-cold then it will die. Anyone have these problems before? what could be causing them? also, at idle, it's at about 800, but fluctuates5-600 rpms(as in it's anywhere from 500 to 1100 rpms), is that normal? any information would help. I was told by the previous owner that it was all in the carb, but just to be sure I'm asking all of you thanks!!

update!! I adjusted the mixture, and the idle speed after that, and guess what? It's like a new car! well, not quite, but it holds idle all the time, the hesiation is now just in the transmission(down shifting) so I'm happy. I probably should've checked the mixture before I even posted the forum, but I figured that was too easy of a fix for it to be true.. also, as a side note, I brushed some corrosion off of the connection for the temp gauge because it hadnt been working since I got it and even the last owner said it hadnt been working, and it now works. if I come across anything else, I'll let you guys know!