The GT 1030 has no hardware encoder if I remember correctly, so you'd have to use software encoder (x264) in your OBS or whatever you use.
This means your processor will be used for compression of the stream, so your games will have less CPU available for themselves.
2200g and 2400g would be cheaper, but I'm not sure OBS and other streaming products support the integrated graphics as hardware encoders.
So my advice would be to simply go for a higher end processor like Ryzen 1700 (8 cores, 16 threads) or Ryzen 2600 (6 cores, 12 threads) which will give you plenty of cpu cores for the software encoding. SInce you have the GT 1030, you can use it strictly for playing games.
i5 8400 is 194$ on Newegg, while Ryzen 1700 is 170$ and Ryzen 2600 is 165$ ... Ryzen 2600 is probably around 10-15% faster than 8400, and Ryzen 1700 is around the same performance as 2600 (you get more cores, but they run at slightly lower frequency).
Strictly on that configuration, you can probably save some money by buying a single stick of memory (yes, you'll lose a tiny bit of performance now by not having memory in dual channel mode, but maybe in a few months you could buy a second stick)
You'd also probably be able to save some more money with a cheaper power supply, but not by much.
Also, you can overclock both, so you get more performance, while with i5 8400 you're stuck at those default frequencies.