I want to change the default weapon slot for some classes. In particular Medic's offensive primary weapon is an odd choice, practically in all instances I switch to the secondary slot (healing) after spawning.
You can enable the option to remember your last used weapon. As I recall, it's in the Advanced Options menu.
Still, the first time you spawn during a map, you'll have to manually switch.
On a side note, the default item is always your primary weapon. That might confuse people who play Spy because it defaults to your knife... but if you've ever looked at the Spy's slots, his revolver is his secondary weapon.
As far as I know, it's not possible to spawn with your secondary weapon already out. The second best thing I could think of is enabling Quick Switch. If you have it enabled you can switch between your weapons by pressing 'Q' more easily.