Yes I know I always say this but, go for a sporter with 30 inch barrels and engraving on it because if you shoot clays the extra 2 lbs in weight of the sporter will help with recoil dampening thats why they are heavier.The 30 inch barrels will help you swing better and is more pointable which helps to get onto the target. Get one with engraving on it and it looks like a game gun when out on a formal shoot. I`v been asked this question a thousand times when coaching and its always the same answer. Only buy a game gun if you are only going to shoot game/rough. The constant recoil on a 100 bird clay shoot using a game gun will have a very negative effect on you in time, it does with a sporter but its not so bad.
I have never had anyone come back yet and say I wish I`d bought a game gun. I have had people say I dont use my game gun much as its too light, I prefer my sporter.
Recommendations would be as follows.
Beretta 686E in black.
Beretta 686 Silver pigeons / 687 sporters.
Miroku mk38.
Browning B525.
Winchester, select sporting.
In the budget bracket.
Lanber deluxe sporter in black.
Bettinsoli, check them all out.
Lincolns.
Get someone in the know to check your eye dominance aswell, it will make all the difference to your shooting.
Spend as much as you can afford.
Dont be worried about second hand, there are some awsome bargains out there in the second hand market but take somone with you if you can with a lot of experience from a club, their advice will be very handy.
Good luck and let us all know how you get on.