Well, i mostly agree with you, but you can also go with i5 2500/3570. They are still better than any recent Pentium. But, this is just me
. Im kinda into older tech. I recently upgraded my old lga 775 rig, E7200->Q9505(18$), 4gb ddr2 800mhz->8gb ddr2 800mhz(two 2gb sticks for 8$) and the GPU(8600gt->gt 1030 68$). 94$ and i got pretty decent low-budget gaming rig.
You can do the same going with used i5 and getiing HUGE perfomance boost, then stick with 1030 for a half year and get smth like 1050 or even 1050ti early 2018.
EDIT: sorry for bad English, i think i messed up some grammar and structure of the last sentence