This is one of the few areas where I seem to disagree with Sprout, but thatās likely due to what weāre used to and our work/travel/lifestyle requirements.
A good laptop makes a great workstation when connected to a large desktop display. For typical graphic design work, a desktop machine has no particular advantages other than significant cost savings, which, depending on your budget, might be the deciding factor.
What a laptop does offer is portability and a second display when connected to a desktop monitor. If these two things arenāt important to you, a desktop machine is probably the best bargain since they cost less. All things considered, Iād personally go the laptop route.
As others have said, 16GB of memory is probably adequate ā for now. If you can afford it, though, Iād opt for 32 because youāll likely need it in two or three years. As for disc space, a large SSD is great when paired with an external drive for storage (I donāt keep many things other than applications on my computerās SSD). A fast processor is also important, but thereās no need to go overboard with it. The extra cost of the fastest processors doesnāt result in noticeable performance enhancement on typical graphic design projects.
You mentioned mostly using Illustrator and InDesign. If thatās the case, the specs Iāve mentioned above are enough. For that matter, theyāre also enough for Photoshop. If youāll be using Premiere extensively or regularly working with animation or 3d modeling, youāll need more of everything.
I see no need for an eGPU for typical graphic design work ā seriously, no need at all. If gaming is a big part of your routine or, as already mentioned, video editing and 3D modeling become mainstays of your computer use, it might be something to consider. Otherwise, Iād put the money saved into more memory, additional external storage/backup, software, or peripherals, like a good printer or drawing tablet. Even a more comfortable chair seems like a better investment than an eGPU.
I have no idea how youāre managing on a 1.10 GHz, 4 GB RAM machine. Thatās barely enough for the operating system.