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At low costs, such as 500 and under ( what I'm looking for) does building my own PC make a difference? I was told it doesn't.
Who ever told you this lied to you.
It ALWAYS matter what you will be doing on it. If it didn't, LTSB/LTSC Windows 10 machines wouldn't exist.
Anyway, I googled their system requirements for you:
Operating Systems
Windows 10
Windows 7 Service Pack 1
Windows Server 2016
Windows Server 2012 R2
Windows Server 2012
Note:
Windows 8.1 is not supported as of R2018b.
Support for Windows Server 2012 and Windows Server 2012 R2 will be discontinued in a future release.
Processors
Minimum: Any Intel or AMD x86-64 processor
Recommended: Any Intel or AMD x86-64 processor with four logical cores and AVX2 instruction set support
Disk
Minimum: 2 GB of HDD space for MATLAB only, 4‑6 GB for a typical installation
Recommended: An SSD is recommended
A full installation of all MathWorks products may take up to 23 GB of disk space
RAM
Minimum: 4 GB
Recommended: 8 GB
For Polyspace, 4 GB per core is recommended
Graphics
No specific graphics card is required.
Hardware accelerated graphics card supporting OpenGL 3.3 with 1GB GPU memory is recommended.
GPU acceleration using the Parallel Computing Toolbox requires a CUDA GPU. See GPU Computing Support for details.
These are the MINIMUM requirements, regardless of what they recommend, I can tell you from experience that recomended is the minimum for functional use. While minimum listed are what's required for it to run.