Ideally, I would like to go from the body shape I have now, to one that would be described as "wiry." Is this possible?
I doubt very much that you can go from "stockÿ" to wirey, because you can't change your overall body type (you have mom and dad to thank for that). For example, Gwenyth Paltrow will never look like Rosie O'Donnell or like Calabrina, a background exerciser in Sharon Mann's show on Fit TV, and vice versa, but you can change your body somewhat to get the 'best possible results' for you.
Since you bulk easily, you might want to avoid any heavy weight work for the legs. Stick with body weight work (which can be very effective, especially if you do lunges and 1-legged work). One style of training, called Freestyle (there's a book on it you can check out), has you work the lower body with very light weights, most days of the week, and emphasizes lunging, with little or no weights. The theory is that you increase strength, but keep the muscles from growing much because you don't give them time to repair (it is a technique that is used with figure skaters, who need strength without much bulk). A workout series on video that has somewhat this approach is "Slim Series."
Also, as CollegeB suggested, keeping weights low and reps high.
You want to get strong, but not big, and to do this, you pretty much have to do the opposite of what someone who wants to add size should do. Many bodybuilders limit their cardio, because they don't want it to eat into their hard-gained muscle and they want the calories they take in (which they increase) to go towards muscle building, not towards cardio energy. So YOU should try doing more cardio, and when doing weight workouts, combine them with cardio either as a circuit weight/cardio workout, or doing what some refer to as 'aerobic weight training": using light weights while doing cardio moves.
And that "get long, lean muscle" stuff: it's just a marketing tactic used by people trying to get you to buy their workout programs or products on TV, because they know that many women fear "bulking." There is no way to 'lengthen' muscle, unless you put someone on a torture rack, but that's no fun!