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I answer the question, about your $1500 three years later, but I think you have all ready bought your fast computer. In 2014 a fast computer should have a SSD Hard Disk >= 120 GB or more, 8-16 GB RAM DDR3-1600 or better an i5 or i7 for the consumer section makes not a great difference which CPU you have. The graphics card is not important if you only want to draw some of your plots the build in graphics card of the i5 or some models of i7 is enough, but an Nvidia or AMD Graphics card is also a good option.
About GPU's power, yes it is true in some cases the GPU can speed up computation extremely, but this works not in all cases. Today (year 2014), their are only a few programs that uses the GPU power for calculation, because it is difficult to write software for combined GPU <-> CPU power usage.
It is important to say, today you could use Sagemath Cloud for your computation. On Sage math cloud you could use a lot of power if you want Sage math cloud limits
As Kelvin Li says, if you really want to compute fast use Linux, because Sage works really fine with Linux. Linux Distributions that I know which has a nice Latex and Sage support are:
Manjaro Linux (Arch Linux for) - which has up-to-date Sage packages, also Latex (texlive-*) packages, a really high quality documentation and a dedicated community.
Fedora - which has up-to-date Sage packages but they are some minor versions behind the latest packages, good Latex support (texlive-*)
Ubuntu or Linux Mint with the additional PPA-Sagemath-Repository , both have a good Latex support and a large user base
