Either you wait for these guys who know the math, or you take the easy-going approach I can offer.
So, the inhabitable world should be at least as heavy as Mars (in terms of mass), but better be in the same weight class as earth - less mass would allow fancy jumping combat, but you may lose your atmosphere, more mass would... do many things. To break things down: aim for a surface acceleration close to ours to get the most earth-like appearance. Something between Earth and Mars in terms of mass and size may work. When in doubt, add superheavy elements to the core ;)
About the other protagonists... here you should aim for something similar to our system. Bigger suns may offer brighter days but also more radiation... which may be nullified if your Earth-Moon is inside the gas giants magnetic field. At the other hand that would mean that it will so close the rotation went to a bound one (one side is facing the gas giant all the time). Just the same our very own moon (Luna) is doing after all. When you want this moon to have a more earth-like rotation, it have to reside in a pretty big orbit, but... I thing there might be a limit of some kind. Here the guys with the correct formulas on hand can offer better explanations: how far it can go of without saying farewell to the gas giant completely?
So, have a modest sun, place that gas giant inside its habitable zone, add a moon that is a bit smaller than Earth but a bit bigger than Mars and here we go. Should work and can offer pretty impressive polar lights under the right circumstances.
Something more: big gas giants will heat up your moon by their own. Not like a true sun, but sufficient to shift the orbit a bit more away from the sun. If you install a brown dwarf instead, chances are high that life would flourish even outside the habitable zone up to some million kilometers. But it would be pretty dim all the time.
Oh... math. As Aaron Lavers in his comment said, you could look up whats happening with the big moons in our system. The gas giant might need more or less a year (less, if the sun is smaller than ours, way more if its bigger, when its orbit is adjusted to stick inside the habitable zone). The planet of yours (the moon)... I guess he will take more than a month for a full round, but way less than a year. Three to four months (real earth months)?
Seasons would be pretty interesting, by the way, because you may have some days your moon would stick in core-shadow of the gas giant. Reminds me about the movie Pitch Black with Vin Diesel.
Well... to stick with the four month orbit (its good for explanation), you would have one month for northern hemisphere for Winter, one for Spring, one for Summer and one for Fall... and imagine the gas giant need twelve to orbit the central star and have some orbital excentricity of its own, you could have three "winter" which range from "cold as fu**" to "pretty hot", while three times a year you suffer from total darkness for a couple of days... If that happens in the "cold-winter" your people would be... very poor off, while in the "hot-winter" it could be more decent. At the other side during a "hot-summer" they will enjoy the off time from scorching temperatures.
To conclude this: your moon will have summer, fall, winter and spring three times a year, one in a hot variant, one in a cold variant, one in a medium variant... and I thing these will shift over the years. Correct calculation will be a nightmare if you decide to go for super realistic orbital times... Maybe its a good idea to stick with the 4-months orbit for the moon and the 12 (or maybe 16) month orbit for the gas giant, so you can determine more easily how things are looking at that moon.
EDiT: Turns out I forgot something: to have long orbital times for the moon, that gas giant can't be pretty big (the bigger, the faster you have to run on your orbit to avoid crashing down). So either move away from the giant (which will make the ecpises less intense), or shrink the giant... hm. Titania from Uranus does have a similiar orbit to the one our moon has but still, it just takes about a week to do a full orbit. That will be tricky. Maybe a 4-month orbit is way outside any posibillity after all... or the gas giant would be as small as our moon at the night sky and lose its appeal ;)
Expect giant tides. And bright nights. The latter will only occur when your moon is between the gas giant and the sun. When its a bright ball of Helium and Hydrogen like Saturn, Reflection will cause nights that are as bright as days (with a few lumen off), while something more... Neptunish will cause more dark nights.
As soon as your moon is behind his gas planet (lineup: sun-gas-moon), nights will suddenly get pretty dark and even days can get very dark, when the moon goes for a full sun eclipse.
Well... enough for now. Coworkers already starting to wonder why I'm this busy typing all of a sudden. My answer might not be the most accurate, but I hope most effects had been covered so you can start expecting how thing would look like. Now wait for these guys with the formulas and small pictures of orbits. Or drop all this, because if its a fantasy-world without modern technology stuff like this wont matter enough to waste lines describing accurately how the solar system does look like.