Depends greatly on your definition of best.
Most reliable:
- Upgrade all the plugins you can
- Upgrade to next jenkins stable release
- follow Jenkins LTS Upgrade Guide
- Upgrade all plugins you can
- Repeat until you are at the most recent version
Easiest Shortest:
- YOLO
- Make a backup of your config.
- Install latest into a new directory/server/etc
- Copy jobs from old one
- Startup jenkins
- Install all the plugins you used to have.
There’s no quick and easy and reliable way to upgrade 251->387 which is about 136 weeks, so 2.5 years of changes.