i5 is a good base to start. I always felt the dual cores (i3, Pentium, etc) were not enough, quad cores too much. I suspect the optimal number of cores is e (2.717). So if you're going to err, do so in the direction of having too much (quad core) rather than not enough. The new hexacore i5s might be overkill, but they come in at similar price and power consumption as older quad core i5s, so there's really little downside.
8 GB of RAM is currently a good starting minimum. You might want to get 16 GB to future-proof yourself. But RAM prices should be dropping this year (they've already fallen about 30% from 2018). So you may be better off just getting what you need now, upgrading in the future. Check task manager (ctrl-alt-del) on your current computer, performance tab, and see how much RAM you're typically using. For most people it's around 4-6 GB, so 8 GB is a safe starting amount.
You've already got a SSD, which is the single biggest speed boost you can make to the computer. So you're good to go on that front. Make sure you have an external drive for backups. (Backups should be offline so ransomware doesn't encrypt it, and stored in a different place than the computer so a fire doesn't destroy both.)
As you'll probably be using the CPU's integrated graphics, make sure the monitor headers on the motherboard match the inputs your monitor can take. Displayport (motherboard) to HDMI (monitor) is relatively cheap. But going the other way can be rather expensive.
For a basic non-performance build, you might want to keep an eye out for sales and discounts on prebuilt systems, rather than build your own. Often retail stores sell systems at below the cost of components during sales. I picked up a couple i5 systems from Staples on clearance for $230 last year, when the price of the CPU alone was $215 from Newegg.
You can also monitor the outlet stores for Dell, HP, Lenovo (google it) to see if a cheap refurb system becomes available. Beware that you'll probably lose the extended warranty and other protections your credit card provides if you buy a refurb. ("Refurbished new" = new custom system whose order was canceled. "Scratch and dent" = cosmetic flaws. "Return" = customer return.)
Other than that, keep an eye out for future expand-ability. A lot of these cheap systems skimp out on number of PCIe slots, number of SATA slots, number of RAM slots, places to mount additional drives.