I've recently done about 8 EE1 to EE2 upgrades. For the most part everything went really smoothly. The key is to prepare and backup, backup, backup. Did I mention you should backup?
Use the native upgrade wizard and be sure to follow the instructions carefully. The download for structure includes a separate folder for upgrading structure 1 to structure 2. It looks scary on the surface but if you follow the instructions exactly everything will be just fine.
My basic procedure with structure is.
Any field types that do not have EE2 equivalents should be converted to a basic text field before upgrading. (if you miss one and find it post upgrade, convert it in phpmyadmin then change to correct field type in CP)
Upgrade EE1 to EE2
- upgrade Structure 1 to structure 2 (don't forget to do the prepping
step while still running EE1)
- Then for any ngen fields or matrix with ngen follow the instructions
in this SE thread (my answer).
- Next install any addons you need (remember EE1 addons are not
compatible with EE2)
- find replacements for addons that do not have an EE2 upgrade option
with nearest equivalent and then check your template code.
I see that Paulo was typing at the same time as me. He has some addional steps which I didn't need, but will still be worth checking out.