-7th gen intel is ONLY a gen behind. Literally no point in arguing about "Oh, 7th gen is old since 8th gen came out". The performance difference is neglible, only core count, and most games don't use more than a few cores. On top of that, Everything is hit by meltdown/spectre either way. Even if most of the performance difference will lie in syscall operations(virtualization), both get that small penalty in general usage.There's nothing wrong with staying one gen old. If a Haswell Chip was suggested, that's another story.
I am not saying it is wrong to go with 7th Gen, I just think buying new is better value and better upgrade path.
-A gen old i5 is VASTLY better than the r3. Making the r3 a low aim is fine, but I would think you put too much faith in single generation gaps to call a i5-7400 a low shot.
Please explain "vastly"
Memory: *Team - Vulcan 8GB (2 x 4GB) DDR4-3000 Memory ($102.99 @ Newegg)
OP wants 16 gb ram
Not too vastly, but i5 7400 is still better.
16 GB ram is what I recommend too, but the budget and pricing in Bulgaria is too tight, so 8 is not a bad option for now.