I have a Trek 7000; regarding your requirements...
1- Be able to do a 24 mile round trip 3-4 times a week, and hopefully not break down with regular maintanence.
I do a 12 mile round trip 3-4 times a week, and it's done fine since October. I've done minor adjustments and have lubed the chain two or three times in the past six weeks.
2- Be... for lack of a better word "effeicient" on large hills.
The 7000 is okay. I've adjusted the saddle and lowered the handlebars, which seems to help in this regard. Developing the engine has made the biggest difference. =)
3- Be sturdy enough to carry a large enough amount of weight on a rear pannier.
I have a rack and a couple of panniers, and I load about 15 pounds into them, plus myself.
4- Hopefully be stable enough in wet weather, seeing as in N Ireland that's all the weather seems to do.
I've ridden after a rain (on wet leaves) and have been fine, but I don't ride in the rain - yet. You'll need to add fenders; SKS P45's (which fit and look good with this bike) cost US$35.