you dont need an emulator to play psx games on the psp... the game needs to be put into an eboot format from a disc image. then the psp will be able to read the game
there is a few things that you will want to do if you are looking at having psx games running well on your psp..
first of all i suggest getting popsloader.. check out this link and follow the guide
How To: Install Popsloader on 3.80 M33, 3.90 M33 - eXophase.com Forums
now the next thing you need to do is create your eboot.. there are several programs which do this.
many ppl swear by PSX2PSP and it is a great. however i personally use RS-GUI PopStationMD v3.00 most of the time..
here is a tutorial on how to get that up and running
PSP Hacking Guide - Part 7: PSX (PSOne) Games - “PopStation” | Blast Processing
i believe those 2 things will have you well on your way to playing playstation games on your PSP.. and if you are interested in cheats then google search cwcheat and check that out..
also about psx roms.. its not a great idea to ask about those sorts of things as it is a moral grey area since you should only download a rom of a game which you own.. remember that google is your friend and i can not give you any links in order to download games..