hard start when warm

[digdoug2]

1996 K2500 HD Ext. cab long bed 5.7l, 145,000 miles. After sitting overnight, it starts right up...idles high(1500-1800) for about 15 seconds and then settles down to normal idle and runs just fine. After warmed up, it takes a while to start(approx 3-5 seconds), then another few seconds to straighten up and then runs just fine. Its been doing this for a few months and I only use it on weekends. This past weekend, it still does everything else the same, but it now idles a little rough and the SES light comes on periodicly. Still runs fine during use. I have recently replaced the fuel pump because it quit working, which didn't change any of the other problems. Any thoughts prior to me getting the SES light checked? I have heard possibilities of a water temp sensor?, fuel pressure regulator, vacuum leak? I would really like to try and fix this myself, if possible, but I don't know where I should start on this one. Its probably a combination of one or more things Thanks, Doug