I use pcsx2. So does everyone else pretty much.
I used the download on their website about 2 years ago and had no problems but I have no idea if it is safe now. Might be some PUP optionals in there somewhere so be careful. http://pcsx2.net/
You can download the console bios from a few different places. Not that I am advocating doing this. I have no idea of the legality of downloading bios files. Downloading ROM files and ISOs of games even if you own the game is still illegal in the UK so I don't recommend doing it at all.
If you do a quick Google search of "ps2 bios" I'm sure you will find plenty of download locations.
As with everything else, scan the files and be careful. Download at your own discretion.