Well, I was in your shoes a year ago, when I started learning Japanese just to read visual novels. First of all, learning Japanese grammar is a must, because otherwise, even if you look up the meaning of separate words in dictionaries, you still won't know how these words affect each other while the slightest variation in grammar can change the whole meaning of a sentence. After learning grammar, I'd recommend trying a visual novel you like rather than one which is easy to translate. It's how I started and I have no regrets about it. No matter what you read, it gets easier with time. It would be worse if you forced yourself to continue playing something you don't like and lost motivation because of it. However, if you insist, I can tell that the easiest VN I've played so far is "Seishun Hajimemashita!". It was so easy that I almost didn't look at the VNR window while playing since I could understand both written text and speech.
I'm a Japanese beginner myself, so I can't recommend games yet. However, I've been playing IkeMen Revolution - Edgar's route (in Japanese version duh ). It wasn't a breeze, but the vocabulary are mostly common and/or repetitive in the first few episodes that I play. Grammar is very basic too, with quite a number of ます/です or simple casual forms that are mentioned in Tae Kim Grammar guide. Also, only commonて and た forms have shown up.
I've only been learning Japanese for a month with Minna no Nihongo I (right now I'm at chapter 9), so I think my level is indeed beginner.
Though I have to admit that I can only use 1 out of 5 free tickets each day
After playing Brothers Conflict for some time, I can include it in the list of games easy for a Japanese beginner. Both words and grammar are really simple. Also, since words often repeat, you memorize them after a while and don't have to rely on text hookers and dictionaries much for the rest of your playthrough.