Welcome to TFL, Compromise!
You've chosen a great screen name for your question, because every carry gun is a compromise between size, weight, and comfortable shooting. This is especially and particularly true about guns that you learn to shoot with.
A learning gun should not be super small or super light. It should not be too small, because small guns are very difficult to shoot well. It should not be too light, because light guns produce a lot more recoil for their caliber than you would expect. Very small guns and very light guns can to make it difficult to hit your target, uncomfortable to practice, and difficult to learn how to manipulate the gun's controls.
On the other hand, a gun for concealed carry cannot be too large or too heavy, because it can be difficult to conceal a large, heavy gun. The exact size of weapon that you can comfortably conceal will depend on a lot of different variables – where on your body you intend to carry, how well you choose your holster, and whether you have a good, solid belt (or other way to attach the gun to your body). It also depends, of course, on your own physical dimensions. Larger people have different concealment challenges than smaller people do. Your shape matters, too, and that's not the same thing as size. But those are all nuances that you will explore as you learn more about concealed carry. For now, it's enough to know that many factors affect the size of gun that you can comfortably conceal.
Beginners to concealed carry often make one of two major mistakes. The first mistake is to go with the lightest, smallest gun that they can possibly choose. For example, the most common bad gun choice I see among women: choosing a lightweight J frame revolver. A revolver may be a good choice for you for many different reasons, but to choose one that is very small and very light for your first gun would be a painful mistake. Starting out with a J frame tends to create people who are not enthusiastic shooters, a kind of self-fulfilling prophecy where someone recommends the revolver because they are sure that you will not want to learn anything about shooting, and then you end up with a gun it's no fun to shoot, and voilà! – You didn't learn much about shooting, because the gun hurts your hand when you shoot, you can't hit the target with this experts' weapon, and you don't find shooting fun. Funny how that works.
The other mistake beginners to concealed carry can make is to go with a large, heavy gun that's too big for their body, clothing, lifestyle, or gear. Typically, this happens because they want to go up to a big caliber – a.44 Magnum, say, or maybe someone told them that "all good defense guns start with a four" - so they end up trying to conceal a gun that is a bit too large for their own physical frame, or for the clothing choices that they prefer. You do see this mistake sometimes among women, but it typically happens only to women who have a very opinionated, macho man advising them on gear choices!
Compromise is the key here. Look for a midsize gun that is comfortable for you to shoot on the range. Avoid the advice of people who want you to take a super lightweight gun for learning how to shoot. Avoid the advice of people who want you to use a gun that's too large for you to carry. Choose instead something from the "compact" or "midsize" categories. Avoid sub-subcompacts.
If you choose a revolver, go with one that is one size up from a J frame. And make sure it is steel, rather than a lightweight alloy.
If you choose a semi auto (and this is what I really recommend for most new shooters, unless you have a strong preference otherwise), make sure that you can reach and use all of the guns controls. Here is an article from my website about how to choose a gun that will be a good fit for your hand:
www.corneredcat.com/article/choosing-firearms/trying-on-a-handgun/
As for caliber, I most commonly recommend 9mm for beginners. This caliber offers a wide selection of guns and gun types, tends to be the least expensive of the defense rounds (not always, but that's the way to bet most of the time), and produces little recoil for its effect on target.
The drawback with .380 ACP is that far too many of the guns chambered for that caliber are "straight blowback" weapons. That means they produce much more recoil than you would expect for their size and caliber. Because of that design factor, it has been my experience that it's easier to find a comfortable shooting gun that is still concealable when you step up to the 9mm.
Happy shopping!
pax