If you already have some protein shake shit, there's not really any reason to grab something else before you use it up. You're in the beginner stages of lifting; your gains are going to be good pretty much regardless of your macro/micro intake. If you are getting 60g from the shake (theoretically) then you just need to eat some meat/legumes/something with protein at another meal to basically come to where you'll be at your reasonable rate for each day. It sounds silly, but don't just try to replace meals with shakes (you can, but at your stage I would highly recommend against it) and instead look at it as something that supplements meals. Unless all you are eating is like, sugar or crisco or something, you're most likely going to get proteins throughout the day from normal meals. At your size, 100g of protein a day is plenty (and most likely overkill) so knocking 60 out with a workout shake leaves a lot of leeway in what you consume.
In before the keto-kids chime in, but if you are strictly looking for gains, don't skimp on carbs. Don't eat a basket of white bread rolls a day, but don't go super-carb deficient either. Those carbs, especially early on, will give you the energy you need to push your limits much easier.
You're roughly 160lbs right? You want 80ish grams of protein a day (at least) and probably 1800 calories (at least) total. On your lifting days, you'll probably want more like 2200 calories (protein stays the same) and spacing them out doesn't matter because you aren't really trying to control hunger. Your goal is to eat enough, and enough of the right shit, to grow. As much as I like 7-Layer Burritos from Taco Bell, they have a bunch of shit that you don't really need to build muscles with. I'd recommend looking into some extremely basic cooking concepts (pan cooking chicken/fish, steaming vegetables, etc) and try to hit your numbers with those types of foods as opposed to what builders would call "dirty bulking" (eating whatever as long as you have enough carbs/calories/protein/whatever) especially as you are starting out. This builds good eating habits, and keeps you from becoming strong-fat.
The key, that needs to continue to be stressed, is you don't want to be eating at deficit if you are trying to put on mass. You gotta eat, and eat fairly "right," and hit the weights routinely each week. You will get gains by doing sporadic lifting and half-assed eating methods, but getting that shit into order will make your progress immensely more noticeable, which is a huge help in the motivation area.