When I think of a desire, I think of something which is a conscious thought. Examining a particular desire can stimulate a pre-rational feeling or reaction (pleasure/pain), which serves as a guide to whether or how we pursue that desire. Then we can consciously think about our desire and our feeling about it; this is where rationality fits into the Epicurean scheme as I understand it. As opposed to beginning and ending with rationality and squelching the feelings, which leads to very bad outcomes.
I would concur with your characterization between desire and feeling/reaction. I also think that order is correct as well: the desire stimulates a feeling of pleasure or pain. And desires can be anything! The desire "I want another drink" can stimulate pleasure, but if the desire comes after a full night of drinking out at a bar, can you use your rational prudent faculty to say "No, that is going to bring me more pain than it's worth in the morning. I want to avoid that and strive for more pleasure later."
Likewise, "I want to buy this expensive car" is a desire and may bring pleasure at the thought of driving the high performance engine. However, if your other desire is to retire early, can you say, "No, I should postpone that desire and invest prudently so I can retire early."
Thoughts?