The main thing you need for that 2.5.1 to 2.7 upgrade is a good backup of the 2.5.1 site. Then you should be able to upgrade to 2.7.
The 1.9 site is a much bigger upgrade and you have to plan for that. First you should upgrade the site from 1.9 to 2.0.10. Once that's done you need to upgrade the 2.0.10 site to 2.2.11 and do the big question engine upgrade in that version.
Then you can finally upgrade from 2.2.11 to the latest 2.7 version.
The important thing is, copy your production sites to a test server. Then practice the above upgrade on that test server. You should only upgrade your production sites to 2.7 then when you're familiar with the upgrade process and have confirmed that there were no problems during the upgrade on the test server.
http://docs.moodle.org/20/en/Upgrading_to_Moodle_2.0
http://docs.moodle.org/21/en/Upgrading_to_Moodle_2.1#Planning_the_question_engine_upgrade
http://docs.moodle.org/22/en/Upgrading_to_Moodle_2.2
http://docs.moodle.org/27/en/Upgrading_to_Moodle_2.7