You are asking different questions essentially, and are also requesting an opinion.

Let's split these analyses up then I'll add my two cents.

Desktop vs. Server Edition

Which do you want to work with more, a GUI or a command line? Better question, do you want to deal with the overhead of a graphical interface which will need memory cycles and video memory to run (in addition to the extra software you want to run)? Another question: Do you need the GUI for Firefox or a web browser?

If all you are running are server processes I would ditch the GUI and use the Server variant instead. This recommendation is based on the need of graphical interfaces vs. my knowledge of the command line. Most of what servers need is on the command line. The Server edition doesn't come with a GUI installed and is command line driven compared to GUI driven (the GUI is just a graphical front end to run the commands the terminal would need transparently).

If you need the computer for Internet browsing and things which need the graphical environment (line word processors, spreadsheet stuff, etc.) as well, then don't use Server variant, just install the relevant server processes alongside the GUI. Lubuntu will be the 'quickest' GUI for those specs as its lightest weight compared to the other variants.

LTS or Newer Release (Non-LTS)

This is an easier question to answer in my opinion.

The LTS (14.04 currently) has a 5 year support cycle, meaning it gets security updates and patches for five years from its release date. The trade off is that you don't get newer software versions (typically). You trade cutting edge software (and newer features in them) for stability.

The non-LTS releases have a much shorter support period. This means you will need to upgrade to a new OS version very frequently. With each upgrade you run the risk of more things exploding. After the support period ends you get no more security updates or bug fix patches for that release, and have to upgrade. The trade off is that you get newer software versions but may sacrifice the stability of operation / version change differences and having to adapt software for each set of changes.

I suggest using the LTS regardless of Server or Desktop edition.

Performance Comparison between 14.04 and 15.04

I have no basis for comparison. However, the GUI will be just as slow in 14.04 vs. 15.04 and will operate at similar speeds. (this applies to 14.10 as well but as that EOLs in a couple months I would not use it) Use Lubuntu with the LXDE environment for the lightest GUI (it won't lag or be slow as much compared to Unity on Ubuntu).

The server software will run about equally fast between 14.04 and 15.04. The huge main difference between 14.04 and 15.04 is the init system - systemd is in 15.04 as primary instead of upstart as the primary. The other big comparison point is the kernel version as well as the software versions available in each release.

However, for just server functions, both will operate about equally well compared to each other.

My Opinion

If all you're running on this is server processes, like TeamSpeak server or a file server, and nothing large scale, it's up to you. However, I would suggest using 14.04 LTS Server.

I suggest this because stability of software version will likely be more useful than upgrading every new release. I also suggest this because the graphics overhead is nonexistent and you have more resources freed up to the system and server processes.

If you want a GUI though, use Lubuntu 14.04 which has the LXDE GUI which is relatively lightweight compared to Ubuntu or the other variants. It also will likely get core security updates for 5 years as well.

You should consider using newer equipment for GUI stuff, though. GUIs are fine and all, but they add additional attack vectors on servers, and with the hardware you have listed GUIs will still likely be slower than on newer, more updated, hardware.