Noted you were intending to solder the connection from the fan to the wires in the junction box? This seems a bit extreme! It makes it very difficult to remove, as you have to cut the wires off, or risk weakening the insulation by the heat from the tip of the iron. The wire nuts should easily suffice.
The hum from the fans can be from radiated vibration noises through the joists, or just generally poor manufacturing. Most fans have capacitors installed inside the switch box to suppress AC noise; these are not always adequate. Try the balancing trick - most new fans come with a small kit for this purpose. Beyond this, ensure that if you have a speed controller that is mounted in place of your light switch, that it is one compatible with the fan and made by a solid manufacturer - Lutron is a good source.
If none of these solve the problem, it is unfortunate but the only remedy would be to return the fan and try a different model.
On another note - read my post at http://www.electricalrepairlinks.com
on Cold Heat soldering irons - navigate from the menu link "my projects" to the blog. You might change your mind - or just prove me wrong....