In short, you're very likely not going to be able to gain weight without gaining at least a little bit of fat. Likewise, you're not going to be able to lose weight without losing a least a little bit of muscle. This is why bodybuilders work in bulk/cut cycles.
To gain weight, you have to eat more than your TDEE (total daily energy expenditure). Provided you get enough protein for your body to repair your muscles when you've worked them out, it doesn't much matter whether you get the rest of your calories from carbs or from fat - both are pretty much pure fuel (though some fat is require to properly absorb a number of nutrients).
Controlling how much fat you gain means controlling how many extra calories you consume. You can really only gain a small amount of muscle at a given time. According to bodybuilding.com, you're looking at about 2 pounds a month, if you're extraordinarily lucky and insanely dedicated.
You'll have to experiment to get the exact number that works for you, but a general starting point is TDEE+30% or so. Remember the limits above, and if you find yourself gaining more than about half a pound a week, you're probably eating too much and should recalculate. This helps ensure that you're providing your body with enough fuel to build muscle, without giving it so much of a surplus that you gain a large amount of fat.
In a few months, whenever you get to about where you want to be in terms of strength (at least for now), or you start seeing a little more fat than you'd like. You can start a cut cycle, which will be something like TDEE-20% to help reduce fat, bringing you to your end goal of having more muscle and less fat.