Welcome to the friendliest corner of CGN. There is a lot of accumulated experience in those that frequent this Subforum, and I hope others will chime in.
It sounds like you are just starting out, good for you. You should have many years of shooting enjoyment ahead.
Your choice of first shotgun, for clays and hunting, depends more on the amount of cash you're willing to spend upfront to get started. Every action type has advantages and disadvantages, and all have ardent devotees -- so advice on type will be varied, too. All will do the job and bring you pleasure, and every gun today is the result of many decades (or a hundred or more years) of design evolution and perfection. Not all are made to the same quality, however, and that can cause a big hit on enjoyment. Budget-priced guns are made to sell, not perform or outlast; they are also most likely to frustrate and disappoint. Whatever type you choose, quality should be very high on your priority list.
Much is said here on fit, which is a valid concern. Best if you can try different guns, and, better still, if this is combined with helpful advice. But for casual use, most guns fit most people just fine, at least while you get the hang of shotgunning.
If I may impart some unsolicited advice to someone new to the sport, it would be this: whatever gun type you choose, treat it as a single-shot for as long as you possibly can -- it will make you a better shot. It is tempting to fill up the magazine on a pump gun, and crank away at flying targets (why else get a pump?). This is the best recipe I can think of to rack up miss after miss. Your brain is thinking about cycling the action before the first clay/bird is hit, and there is not enough concentration to really get the first, or second, target. I am within hearing range of a duck marsh, and every shot I hear is bang-bang-bang. I can almost guarantee each attempt is a miss. A second shot should be for the second target, not to correct a (likely) miss on the first. When you only have one shell in the gun, it does a remarkable job of focusing your mind on the target, as you only have that one chance. Become good at wingshooting, and clay birds and hunting become terrific pastimes. Get frustrated early on, and you're more likely to drop the sport and move on. There are excellent books, and more-than-likely YouTube videos, on wingshooting, if you don't have friends who can help. Just remember that proper gun placement and timing are of primary importance when it comes to hitting targets, not choke selection or magnum loads (my opinion, for what it's worth).
If you go the pump route, a 1950s-1960s era Ithaca Model 37 or Remington Model 31 would be my choice -- properly machined metal, too costly to do nowadays. There are equal arguments to make for a Winchester Model 12, or the older Remington Wingmasters. All of these second-hand guns can be had for the same or less than a new budget gun, the difference is that they were made with much higher quality materials and methods. Newer pumps are made in factories run by accountants.
