Choice of gun The best gun to shoot is the one you shoot best with.
Many shooters use a 20 bore, some will even shoot successfully with a 28 bore, more typically you will be using a 12 bore. In most situations, a standard game configuration is adequate.
For most game a 30g load of No6 for the first half of the season is appropriate, for the latter half of the season this may move to 32g or 34g of No5
If using a 20 bore then a minimum 30g loaded with No5 is appropriate.
Never underestimate how many cartridges you will need, 250 may not be sufficient for a good day, keeping spares in the car/vehicle is always a good idea.