We have clients looking along the same lines.
And for about the same money, you can purchase a more powerful model
HP Business Desktop ProDesk 600 G3 SFF Computer - Intel Core i5-6500 3.2GHz / 16GB RAM / 512GB SSD/Windows 10 Professional (Renewed)
Well some of our clients, lean more towards this Dell model
Dell Optiplex 7040 Business SFF Computer Small Tower PC (Intel Core i5-6500, 16GB Ram, 256GB SSD, DVD-RW, WiFi) Win 10 Pro (Renewed)
To perform properly with Illustrator, it will need a dedicated graphics card
AMD Radeon RX 550 4GB GDDR5 PCIe DP 2 x Mini DP Low Profile Graphics Card R9J9P
This card will work with both models. Although it is suggested to get quality cables, depending on the monitor or television you're connecting it to.
Silkland DisplayPort 2.1 Cable [16K@60Hz, 10K@60Hz, 8K@120Hz, 4K@240Hz 165Hz 144Hz] 80Gbps HDR, HDCP DSC 1.2a, 6FT
ULT-WIIQ 8K DisplayPort 1.4 to HDMI 2.1 Cable [8K, 4K@120Hz/144Hz, 2K@240Hz] Dynamic HDR, Dolby Vision, HDCP 2.3, DSC 1.2a, 6.6FT
Although not definitely required, most people run in Adobe eventually upgrade to 32GB
Timetec 32GB KIT(2x16GB) DDR4 2133MHz PC4-17000 Non-ECC Unbuffered 1.2V CL15 2Rx8 Dual Rank 288 Pin UDIMM Desktop PC Computer Memory RAM Module Upgrade (32GB KIT(2x16GB))
But you can basically be done at any point.
Hope this information helps
MaxProAndU Team