How do I decide what version of Ubuntu to install?
To help you choose the right version of Ubuntu, just head to the Official Ubuntu current releases site.
If you want the most current stable version of Ubuntu and don't like problems just start reading from the top of the list and stop when you see the first LTS (Long Term Support) version and download and install that.
If you're a bit of an Ubuntu hobbyist or like upgrading often (at least once/year, more if you can) just start reading from the top of the list and stop when you see the first version and download that.
If you're a pioneer and want to help advancing the human race just start reading from the top of the list and stop when you see the first version that says future (Warning: you might want to install this version in dual-boot with a stable version)
So, please don't install "Dapper Drake" or "Utopic Unicorn" just because their names sound cool!
The number of the Ubuntu releases represents the date of their publication.
For example:
Ubuntu 14.04 has been released in April 2014
Ubuntu 13.10 has been released in October 2013 and so on.
The versions with code xx.04 where xx is an even number are the LTS versions. These versions are supported for longer then the others.
People that want to have always the last features should instead install the most recent version.
On the other hand, people that want to be sure to have something stable and very well tested should choose the last LTS. LTS versions are commonly used in enterprise but also by a lot of people that do not want to update often their system.
I'll second the discussion above but flush it out a bit. I learned something, that even-number.04 are LTS versions and the first time I heard it stated like that.
If you don't like messing and re-installing every 6 months the most recent LTS version is definitely the best option. They are updated for 2 years and you don't have to touch them for 2 years. At this moment it is 14.04. If they work, then why mess with it. This is what I do for my print server EeePC as well as my for my wife's Asus netbook. My wife doesn't want want any hassle and does not push the envelope in any kind of way. She just wants to turn it on and use Firefox, LibreOffice, and watch media.
On the other hand, your hardware may push your choice. I just bought a new Lenovo Yoga Pro 2. 14.04 had several bugs for this hardware (e.g wifi didn't work) because it is so new. These bugs were fixed with the next kernel release that came with 14.10 distro. Even if this was my wife's computer, 14.10 was better for this particular hardware.
The down side is that the non-LTS versions have a short life span as they stop updating them now only about 9 months after they are released. Therefore, you need to upgrade pretty much on the 6 months schedule.
For me, I love upgrading, it is sport. Every version has advancements and a few regressions. I have gotten good at it and can do it much faster than back in the day. Things gradually evolve and get better and better. An example of the improvements is the touch screen working on the Lenovo out of the box. I have been able to follow the evolution by doing regular upgrades. I do a complete fresh install every 6 months. It also forces me to backup my data every 6 months. The next version coming up shortly will be my 15th version.
Pay your money, take your choice. Personally, in my household, I have 5 computers on Ubuntu. I always use the latest version, be it LTS or not. I choose which version by the purpose for which the computer is used as I outlined above. For my own computer that I use every day I use the latest which is 14.10.