Do I have to update to 8.3.0 first before I can update to latest stable release? I pritty messed up my site by updating my 8.2.6 site as followed.

Step 1: I edit my composer.json file. I replaced the replace to require
"replace": {
        "drupal/core": "~8.3" to

"require": {
        "drupal/core": "~8.3"

Because I wanted to update core and vendor I did this composer command
step 2: composer update --with-dependencies

step 3: Site was broken unexpected error (500) using WAMP 2.4.23, php version 7.0.10 and mysql 5.7.14.

Do I have to update to 8.3.0 first before I can update to latest stable release?
- example: composer require drupal/core:8.3.0
It depends on your modules. If you are using DisplaySuite there is an issue with updating because of the change from layout_plugin to the layout_discovery module. See this issue. And have a look at the 8.3.0 Release Notes for broken changes and affected modules.