What I like to do to find new avatars to work on is go to TDN's avatar lists and sort by least rare first (like this https://thedailyneopets.com/neoavatars/solutions?category=8&sort=commonest for games), since that will show you which avatars a lot of people have. I figure those will be easiest for most people, myself included. I'm personally not great at games but got a few just from playing games I like a lot (like snowmuncher, whack a kass, etc). The puzzle/luck ones are the easiest for me. Not sure if you'd count them as "game" avatars but the ones like poogle racing, grrarl keno, shapeshifter, double or nothing, etc. are pretty easy, just take some time. For the flash games, everyone is good at different ones. I would suggest going through the least rare list and playing each game a few times to gauge your innate skill, and keep playing the ones you're close to the avatar score for.