Liam,
What would I do?
I'm a journo and a historian, not a politician nor a general, so I could only ever do the 'bleedin' obvious'.
1) Prepare the ground. Get the UN fully on-side and issuing resolutions which would give my actions full 'force of law'.
Ensure that my campaign could not be construed as a 'crusade' against Islam. Take advice before describing it in such terms, or allocating stupid and insensitive code names.
Take the necessary action to prove that I (and my nation) was a 'friend of Islam' (eg give Israel and ultimatum to abide by UN resolutions, threatening to cut off all aid, but promising unlimited security assistance if it did pull out of the West Bank and E.Jerusalem. Make the US presence in Saudi Arabia more sensitive and less visible. Think before criticising Arab states, use the carrot rather than the stick to get them on side.
2) Draw up realistic, achievable short term and long term aims and clearly articulate them.
Short term. Destroy UBL's training camps, destroy the Taliban's military capability (if the consequences of the latter are acceptable).
Long term. Get UBL. Fight terror worldwide.
Use the Press. Explain carefully what's being done and why, and explain that civilian and own casualties are likely (perhaps in a broadcast to the nation voiced over images of 11 September). Admit that 'War is hell' and will demean all of us. Explain why it's still justified.
3) Commit the forces necessary to achive the short term aims in the short term - compressing negative aspects, collateral damage etc. into the shortest possible timescale, achieving the aims before public opinion has a chance to waver. EG all enemy airfields and aircraft to be 'taken out' by Day 3 at the latest.
4) Do whatever is necessary to secure multi-national participation and basing. Especially bases in India and even Iran. Commit a minimum of five carriers (Desert Storm level) and achieve at least 300 bombing sorties per day.
5) Wait until these conditions can be met before being sucked into a long and ultimately counter-productive campaign.
6) Attack the target set repeatedly until destroyed, but within a short and finite period. Then STOP.
7) Bask in glory, prepare for inevitable second-term.
8) Try not to smirk!