If you want to start easy, I would absolutely start with an NROM game. The ERPOMs are cheap and there is ZERO rewiring that needs to be done. Just program the chips, desolder the CHR and PRG, replace with EPROMs and presto! You've got yourself a repro.
Many people opt to go with a cheap Willem programmer, but you may as well spend a bit more and get something nice. I've had two and can recommend both.
First:
http://cgi.ebay.com/True-USB-EPROM-c...efaultDomain_0
This one could handle any chip I needed to program for NES repros and it was very easy to use. Unfortunately, it couldn't read a couple bizarre proto EPROM chips I had, so I purchased a higher end programmer.
http://cgi.ebay.com/New-TOP3100-USB-...efaultDomain_0
This is what I use now and it is fantastic. Can program 42 pin chips, can set to batch programming, can auto-detect chip types, and can basically do anything I could ever want it to do. Killer programmer, I really love it.
You'll also need an EPROM eraser. Again, you can get a cheap-o one, but you're better off spending the cash on something nicer.
Good luck, let me know if you need any help!