When 2.2.0 is now out, I will upgrade my current set;
* Apache2.2.3
* MySQL 4.1.21
* PHP 5.2.0
* IPB 2.1.7 (along with IPB/IDM/IPG)

Current PHP and Apache are already at their latest, thus no upgrade needed.
That leaves IPB and MySQL...

Which way is the best?
First MySQL 4.1.21 -> MySQL 5.0.27 and then IPB 2.17 -> IPB 2.2.0, or vice verse?

always do Board before the others

Upgrade ur server first. IPB would be just another software running on ur server :)

So in which order, board or MySQL, PHP first?

At least to me, the most logical choice ought to be;
Start with 'full' backup.
First update IPB (as IPB 2.1.7 officially didn't have support for MySQL 5.x... and IPB 2.2.0 do).
Then make sure everything works as expected (no obvious errors), and from there make a backup (again).
Then upgrade MySQL 4.1.21 -> MySQL 5.0.27.

Please give pros and cons for the different approaches...

If you have just IPB forum installed on ur server and if you are concerned only
with its functionality, then backup > upgrade the forum to 2.2.0 final and then take a good backup.
I didnt suggest you to backup data n sql's as I thought you would be doing that either ways. Wont you? -_-

i plan to do the same but will be upgrading my server first, this includes apache/mysql/php and install eAccelerator then installing the board.