Hey Andrew! Seems like a great idea to upgrade, the i3 is a great choice, however if possible id personally recommend going one up to the i5-8400 counterpart, $80 is a relatively fair price difference.
https://pcpartpicker.com/product/LHYWGX/intel-core-i5-8400-28ghz-6-core-processor-bx80684i58400 
Another recommendation I would like to make is just making sure that the case has pretty high CPU cooler clearance, in case you plan to take the case along future upgrades and easy cable management as it sounds like its your first self-built computer (don't take that the wrong way
How much ram does your computer have, and is it ddr4 or ddr3?
If you want, consider a fairly cheap ssd upgrade to use as a boot drive. (https://pcpartpicker.com/product/2FDzK8/kingston-a400-120gb-25-solid-state-drive-sa400s37120g)
Lastly consider a slightly more powerful power supply as it is only a $3 difference.
https://pcpartpicker.com/product/zNK7YJ/evga-power-supply-100b10500kr
Good luck with your build mate, id strongly recommend spending the extra $100 on the goodies as you get more cores and an ssd (the CPU speed can be overclocked to 4.00ghz if needed.)
Cheers,
lmnvum