Redmine is getting more and more popular and is therefore becoming a tool on which companies want to build their businesses. So, this certainly helps to obtain more and more options for easy installation of Redmine. I guess no one can now say that it's hard to establish a Redmine server.
The easiest way to establish a Redmine website is perhaps by using a dedicated Redmine hosting provider. The problem with this option, however, is that you are limited in the customization of your Redmine instance (for example, you won't be able to install custom plugins). Also, you will have to deal with the customizations of the hosting provider (which you may like though).
One of the oldest and best known Redmine hosting providers (on which even some of its core contributors now work) is https://plan.io/. Their customized Redmine comes with the agile board, contacts, the CRM and helpdesk functionality (plugins of http://www.redminecrm.com/), news renamed to blogs, team chat, and more. Of course, it's not free, but the company offers a free 30-day trial at https://plan.io/.
Another hosting provider became known due to their interesting plugins that can be used for pure Redmine as well (but they are limited and their full versions are not free). It's EasyRedmine. Their Redmine version is highly customized and may come with many different amazing plugins, including plugins of http://www.redminecrm.com/ and of their own. EasyRedmine can also be downloaded and installed on your server, but it's expensive. Luckily, you can try it for 14 days before buying. Their website is at https://www.easyredmine.com/.
There are also other dedicated Redmine hosting providers, such as http://hostedredmine.com/, which offers free hosting; http://www.saas-secure.com/index.html, which offers a limited free hosting service in addition to the paid one; and more.
When I was going to create a DigitalOcean (VPS provider) Droplet with Ubuntu 14.04 LTS for a Redmine installation from sources, I found that the list of pre-installed applications contains Redmine, as shown here:
You just click on it (give it a name) and wait a little for the cloud hosting provider to establish a new server with Redmine that just runs. What can be simpler than this?
However, don't think that I am claiming that this is a unique feature of DigitalOcean. It's quite possible that some other hosting providers offer similar Redmine server images. Just check out your favorite provider for such an option.
The DigitalOcean pre-installed Redmine server image currently uses Ubuntu 14.04 LTS. At the time of writing this subsection, the version of installed Redmine is 3.0.3, what means that the installation was done from sources and that they update the image periodically. Like us, DigitalOcean used the MySQL server and the Passenger module. Unlike us, however, they used Nginx. The installed Redmine does not ship with any plugins but includes the Subversion integration.
As the name suggests, the TurnKey Linux Redmine appliance comes as ready-to-use Linux images that can run under VirtualBox, VMWare, LXC, and Docker or can be deployed on a VPS (OpenVZ, Xen or OpenStack) or Amazon EC2 cloud. It is also available as a live CD ISO image, what means that you can first try and then install it. TurnKey Linux is based on Debian, so after deploying or installing it, you in fact get Debian. Therefore, you can update and install additional packages or security fixes from Debian repositories. However, it is not recommended to upgrade such an installation to the next major version of Debian. To migrate to a newer version of the appliance, TurnKey recommends that you use their special tool called TKLBAM.
The TurnKey Redmine appliance currently comes with Redmine 3.0.3, which was installed manually, and therefore it is not connected to the system package manager. It uses the MySQL server, the Apache web server, the Passenger module, and Ruby Enterprise. The appliance comes with Subversion, Git, Bazaar, and Mercurial servers, which are already configured and integrated with Redmine. Email integration is also preconfigured and the mail transfer agent is Postfix. Besides, the system runs the SSH server, Webmin, and Webshell.
A special mention should also be made of TurnKey Hub. Like DigitalOcean, it allows you to quickly deploy the Redmine image on the Amazon EC2 cloud.
While the basic idea of the TurnKey Linux appliance is to ease the deployment of a new server, the basic idea of the Bitnami stack is to ease the deployment of an application. The Bitnami stack contains everything needed to run the application and, unlike TurnKey, supports Windows and Mac. In addition, you can download an Ubuntu-based virtual machine with the Bitnami Redmine stack intended for VirtualBox or VMware; or you can easily deploy the Stack on Amazon EC2, Google Cloud Platform, Microsoft Azure, VMware vCloud Air, or DigitalOcean. When deployed on the cloud, the Bitnami stack uses different host OSes for different cloud providers, thus for DigitalOcean, it uses Debian 8.1.
Note
By the way, the deployment of a new Bitnami Redmine server on DigitalOcean is almost as easy as the deployment of the DigitalOcean's own Redmine image. But this feature is available only from the following Bitnami page: https://bitnami.com/stack/redmine/cloud. This page can also be used for deployment on other cloud providers.
The problem with Bitnami is that it is separate from the rest of the system, and therefore, you face all the maintenance issues mentioned earlier. Despite what you might expect, upgrading the Bitnami stack is not an easy task (Bitnami even recommends that you simply reinstall it). However, one good thing is that you can deploy other Bitnami stacks on the same server; for example, you can deploy the WordPress stack on the server that is already running Redmine. Another good thing is that the Bitnami stack always comes with the most recent version of Redmine.
Taking the preceding paragraphs into account, I can conclude that the Bitnami Redmine Stack is good for development and testing and it should not be chosen for production. Of course, it's only my opinion, and you should come up with yours considering all the said factors.
The Bitnami Redmine installer comes with Redmine 3.2.0 and everything you need to run it. Thus, it includes Apache, MySQL, Rails, Ruby, Passenger for Linux and Mac, and Thin for Windows. The installed Redmine ships with Subversion, Git, and CVS integration.
The Bitnami Redmine installation does not include any plugins, but Bitnami also offers the Redmine + Agile stack, which additionally includes the Agile plugin of RedmineCRM.com.
The Docker image is much like the Bitnami stack—it's a kind of a container that includes the application, everything needed to run it, and their dependencies. Like Bitnami stacks, multiple Docker images can be deployed to a single host system. But unlike Bitnami stacks, a Docker image is not self-contained. Thus, it requires Docker to be already available on the system to which the application is deployed.
Docker provides a registry of available applications, called Docker Hub, which lists more than 120 Redmine images. This registry includes an official Redmine image, but the most popular one is Sameer Naik's sameersbn/redmine. Both images should be used in conjunction with MySQL or PostgreSQL Docker images.
Note
Links to the images
The official image is https://hub.docker.com/_/redmine/ and Sameer Naik's image is https://hub.docker.com/r/sameersbn/redmine/.
While Docker is a Linux-based tool, it can also be run on Windows and Mac using a special tiny VirtualBox machine known as the Docker Machine. Certainly, this kind of setup is not to be used in production.
As you may have probably noticed, Docker is quite popular nowadays. Thus, it is available as an application on DigitalOcean and is supported by TurnKey and Bitnami (some appliances and stacks can be deployed on it). So, it's not a problem to deploy Redmine on a server through a Docker image.