ePSXe is the best emulator, but you'll have to do some plugin installation and configuration.
Pete's GPU plugins are the best:
http://www.pbernert.com/html/gpu.htm
Go with Pete's OpenGL2 PSX GPU as it's the most recent one and has better compatibility.
These are my settings and they give the best results in Final Fantasy games which have some quirks with other GPU plugins or certain settings:
With these specific settings (especially the "Extended w/o Sprites" setting), even the battle transitions in FF games will work.
The settings are optimized for the best looking graphics, though some of the settings can be turned up even more to get even better results. You might need to turn them down a bit since you have an integrated GPU.
Make sure you enable the setting for FF7/FF8 under special game fixes too.
I use Eternal SPU for sound, there are two versions on here, one beta:
http://forums.ngemu.com/downloads.php?do=cat&id=114
Try the beta first, if you have problems try the other one.
For CD-Rom plugin you can just use ePSXe's built in one.
And lastly, use scph1001.bin for the PSX bios. Use google to find this.
Your other option is using pSX and it requires less configuration and doesn't use plugins but it's very basic and you will probably get better looking graphics by using ePSXe with Pete's OpenGL2 plugin. It does however work well with very little configuration, but I would take the time to set up ePSXe correctly instead as it only needs to be done once and gives a better result.
Edit: However I suggest you play the DS version of Chrono Trigger instead as the PSX version is scaled and blurry.
The Breath of Fire games would be worth playing as well since you like Final Fantasy. Vagrant Story and the Lunar series too.