So here's some stuff to think about, I'll loosely paraphrase and possibly get some of the details wrong:
Intel uses a naming convention that goes like
- Product line: i3, i5, i7 are the good ones, Pentium and others are super budget
- Architecture: 6XXX is Skylake which came out this year, 5XXX is older, 3XXX is a few years old
- Power Draw: Y is very low power (~5 Watts), U (~15-25 Watts), H/HQ (~45 Watts)
A lot of these chips have iGPUs which are part of the CPU(all on the same die), which have their own naming convention like HD5000 graphics.
An Intel Core i3 3XXXH chip is 45 Watts, it isn't as fast as an i7 HQ chip, but it is much faster than an i7 U or Y variant. This goes doubly for the iGPU that is included in those CPUs. So HDXXXX graphics in a 45 Watt i5 would smoke the HDXXXX graphics in an i7 U or Y chip.
Bottom line is go with the 45 Watt CPU if you can, this also improves its integrated graphics (I think, I haven't researched this in a while)
The high power integrated Intel graphics can absolutely run FF7 without a problem, especially if your chip is relatively new. I doubt you'll find a worthwhile dedicated GPU at that price range(if you do, definitely go with that).