On the Intel side the 8350K is not a good choice in terms of optimal perf/dollar. The two options you should be considering are i3 8100 and i5 8400, depending on budget.
On the AMD side the 1500X and 1600 are good alternatives.
On the GPU side I would recommend a card with 4GB of vRAM, since it will age better when using Photoshop and Illustrator in long term (short/medium term 2GB is plenty). For gaming the 1050Ti will be the best choice, but strictly for development and graphics editing anything between RX 550, RX 560, GT 1030, GTX 1050, GTX 1050Ti will work. Don't go with previous gen cards, it's not worth it.
Now, every one of the CPUs above can be ok for the tasks you are considering, so my advice would be to go for the one that properly fits the budget once other components are taken into consideration (SSD, RAM are very important). In terms of platform cost (CPU+MB) you will be looking at them like that i3 8100 < R5 1500X < R5 1600 < i5 8400.
So, recap:
1. Set money aside for a good SSD and min 16GB of RAM.
2. Choose a GPU.
3. Deduct the above from your budget and choose the highest CPU + MB combo you can afford.
4. Enjoy!