What OS and what version of Logic you use? Though, whatever your set-up is, it´s very easy to overload processor with heavy use of third party plug-ins.
Some third party plug-ins are really power hungry – and can freeze any computer. My advice is that try to avoid third party plug-ins if possible, native plug-ins of Logic are great! In some cases better than many expensive and trendy third-parties – and I've never faced any serious problems when using them.
Then, use freeze function, bounce your tracks, use stems etc. – in a nutshell, learn better working habits. If that don't help, even though I'm sure it will help, and if you want a bit better specs, buy a second hand iMac or miniMac. IMHO, the machine you linked is quite expensive, and there's no sense to use extra money for faster processor, that not necessarily help in your case.
Lastly, it can be that your issue is related only to a certain third party plug-in. What plug-ins you use and how? And have you tried to freeze your plug-ins?
Currently I believe I am running the latest version of logic 10.7.0 (when I updated is when the problems began. The latency is the biggest issue and even when I'm recording I hear artifacts like cracks and pops in my vocals.