If you want to use both on the same Droplet, the simplest way would be to use Nginx as a reverse proxy in front of both apps. I'd start with GitLab as it uses an "omnibus" installer which bundles a number of components including Nginx. Many of these bundled components can be configured in /etc/gitlab/gitlab.rb See this doc for more information on how to configure Nginx settings through it.

You can add a custom include directive to the Nginx configuration. This will allow you to set up a separate Nginx config file for your Redmine instance. In /etc/gitlab/gitlab.rb add:

external_url "http://gitlab.example.com"
nginx['custom_nginx_config'] = "include /etc/nginx/conf.d/*.conf;"

You can now create a server block for your main site in the /etc/nginx/conf.d/ directory. Then run gitlab-ctl reconfigure to pick up the changes.

You can also disable the bundled Nginx all together and install the distro version if you want by adding:

nginx['enable'] = false

Now you should be able to install and configure Redmine as you normally would. See their docs on using it with Nginx for more info.