You are probably going to get as many different suggestions as you will responses to this question. They are all likely to have some merit. And you should probably ignore them all, including any advice I offer.
Only you can decide what handgun is right for you and you can only do that after having gained some experience. So the one piece of advice I would take to heart is to go out and try some different handguns.
I have actually found at the local range I frequent, fellow shooters are often happy to let you shoot a magazine through their gun if you are polite and show interest. People like to show off their firearms, and that is one way to do it. There are local indoor ranges near me that have a pretty wide selection of rental handguns in different sizes and calibers, including compacts and subcompacts like the M&P Shield.
The decision making algorithm is somewhat complex. First you need to choose between revolver and pistol. Then you need to select the trigger action. Revolvers will be single action only (think cowboy guns), double action (the most common variety which can be fired uncocked or after cocking the hammer, or double action only, which often have a bobbed hammer that cannot be cocked. Most revolvers do not have an external safety.
For pistols you will need to decide between all-metal or polymer-frame, striker-fired or hammer-fired, and again, trigger action. Single action pistols like the model 1911 have a relatively short, crisp trigger pull that can be made quite light, and virtually always have an external safety or safeties.
Double action only (DAO) hammer-fired pistols have a relatively long and typically somewhat heavy trigger pull much like the DA trigger pull of a double action revolver. DAO pistols generally lack external safeties. There are also "enhanced" double action only triggers like the SIG double action Kellerman (DAK) or Heckler and Koch LEM.
Traditional double action or DA/SA pistols have two different trigger pulls, somewhat like a double action revolver. The DA trigger pull is long and heavier and the SA trigger pull is shorter and lighter (although usually not quite as light as the SA trigger pull of a double action revolver). The big difference between a DA/SA pistol and a double action revolver is that the slide action cocks the hammer after the first DA shot, so that all additional rounds in the magazine can be shot SA without cocking the hammer. Most DA/SA hammer-fired pistols have a decocker lever, and some also have an external safety.
And then there are striker-fired pistols. Some of these are categorized as single action only and some double action only, but the trigger pulls are much unlike those of a single action hammer-fired or double action hammer-fired pistol. They vary in the length and weight of trigger pull, but most are rather more like a single action pistol with a medium to moderately heavy trigger pull than a double action revolver or DAO pistol. Most striker-action pistols lack external safeties, although there are many exceptions. There is also one striker-fired pistol that actually has both DA and SA trigger modes and a decocker button, the Walther P99.
DAO revolvers, DAO pistols and the vast majority of striker-action pistols have a consistent trigger pull length and weight that does not change shot to shot. For so-called DAO striker-fired pistols, slide reciprocation is required to pretension the internal striker. The significance of this is that they typically do not have second strike capability like a DAO or DA/SA pistol. Pulling the trigger will not do anything if the striker is not pretensioned.
After you have decided between revolver and pistol, hammer-fired or stiker-fired, and trigger type, you can then consider size and caliber.
The significance of the trigger type is that it greatly influences ease of shooting and handling safety. Many feel that double action revolvers or DAO hammer-fired pistols offer the greatest safety in handling because the rather long and heavier trigger pull helps prevent an unintentional or premature discharge. Traditional double action (DA/SA) pistols offer the relative safety of the long DA trigger pull for the initial shot with lighter, shorter trigger pulls for followup shots. Many people feel safer carrying TDA pistols with a round chambered, decocked, with safety off (or no safety) than they would a striker-fired pistol with a shorter and typically lighter trigger pull.
In my opinion, the easiest handgun to learn to shoot accurately is probably the single action, hammer-fired pistol due to its consistent and crisp trigger action. But using a single action pistol safely requires an absolute mastery of engaging and disengaging the safety effectively, especially if it is to be used for self-defense. And many people are simply not comfortable with the idea of carrying a single action, hammer-fired pistol "cocked and locked" (hammer cocked, thumb safety on).
In my experience, the second easiest handgun to learn to shoot accurately is the striker-fired pistol with a consistent trigger pull that is generally shorter and lighter than the DA trigger pull of a hammer-fired revolver or pistol. Most striker action pistols also have simplicity of controls with no external safety (usually) and no decocker.
DAO revolvers, and DAO hammer-fired pistols also have simplicity of controls and consistent trigger pulls, but the trigger pull is much longer and often heavier than that of most striker-fired, or single action, hammer-fired pistols. It is simply harder for most new shooters to keep the sights properly aligned during that longer, heavier trigger pull, so these weapons may take longer to master.
Double action revolvers have two different trigger pulls, but if used in a self-defense scenario, they will almost certainly be shot in DA mode only. So if you choose one of these make sure you consistently practice with it in double action.
Traditional double action pistols require mastery of two quite different trigger pulls as well as the transition from the DA to the SA pull, which again can require a longer period of training to shoot effectively. They also have either a safety, a decocker, or a combination safety/decocker lever to master.
In my opinion, choosing the type of handgun and type of trigger action is far more important than selecting the caliber. I shoot most of the common handgun defensive calibers (9mm Luger, .40 S&W, .45 ACP, 357 SIG, 38 Special, and 357 Magnum) and there is something to be said for all of them, but the recoil characteristics can be quite different and very dependent on the size and weight of the handgun. Recoil sensitivity is very subjective, so again, only you can decide on what caliber is most appropriate for you. I will say however, do not consider buying a small and relatively light revolver with the intention of shooting 357 Magnum through it without first trying it.