Everyone has a preference to what gun feels right in their hands. You would be best suited to go to the gun store and get some hands on various pistols first. I usually hit up on of the big names shops that has a good variety and then come on Buds to purchase what I end up liking. Many have already stated the midsize "Glock 19" might be the best choice for your hands. I would stay away from 380 since they are going to be small and the ammo costs are higher. Take your time on the purchase and when you find the one that fits check reviews on if there are different models that have the features that you want. Plus look at the holster options available. I usually find Buds to be a few hundred dollars cheaper and then no sales tax so massive savings on your purchase. Please take your time and find the gun you like or you end up having something that you never carry.

Bersa thunder big enough for your hands; small enough for your front pocket.

To honest if you have large hands, a truly “light weight” handgun is probably not going to be comfortable for you to shoot. Lightweight handguns, such as the Ruger LCP II and similar genre are very small and even I with hands somewhere between small to medium do not find these gun comfortable to shoot. These not a bad handguns its just they are very small and somewhat difficult to shoot. That said the best thing for you would be a compact sized handgun. I have several compact handguns that are not too heavy, excellent quality and have either adjustable back straps or grip modules. I would look at the Glock 19 Gen 4, the Sig P320C. Other options include the S&W Performance Center version of the Shield, or the Taurus PT111 Millennium G2, or Glock 43. These don’t have interchangeable back straps or grip modules, but are moderate in weight and/or size. All of the handguns have good trigger systems shoot very well and reliable. These handguns run the gamut in prices so your budget may drive you to a specific model. I own all of these handguns and my overall favorite is the Sig P320C. For low cost, the Taurus is hard to beat. All of these handguns work flawlessly are moderate in weight and size with the Shield and G43 being the smallest. There are many other handguns out there and everyone has their favorites (and biases). You should visit local gun shops and try different brands/models on for “size” and determine the ones are most comfortable and fit your hand the best.

Look at the S&W M&P 9c, it was prior to the shield, a little wider, great size, great feel, great gun.

If you have very large hands you might as well go with a Glock 19. If you shop around and get a good holster you can conceal it with virtually no problem. I use a Bravo Concealment holster and conceal a full size Glock 17 with a tactical light daily without any issue.If you really want something small, then I'd go with a Glock 26 or Springfield subcompact Mod-2. The larger frame will fit your hands better, plus you wind up with more ammo capacity. Unless you live in a state where magazine capacity is an issue or you absolutely have to have something very small, then there is no reason why you cant buy a nice holster for a slightly larger handgun. I hope you find something that will suit your needs. I have long fingers so I understand that most micro handguns aren't easy to shoot.

If you have large hands you are probably a big enough guy to hide a compact. Spend the money to get a decent pistol that will not fall apart or fail if you practice enough to be proficient with it. The SIG P239 is a good choice.
budsgunshop.com/catalog/product_info.php/products_id/55801/Sig+Sauer+239-9-SAS2B+P239+SAS+GEN+II+8%2B1+9mm+3.6%22

you can go with a bersa 9mm

There are quite a few ways to go with this, but you have to ask yourself a lot of questions.
How do you intend to carry?
What other features are important to you?
Do you value concealability or capacity?
For highly concealable 9mm pistols, you have a plethora of options in the single stack world. The Smith and Wesson Shield, Springfield XD-S, Walther PPS M2, Kahr CW9, and Glock 43 are just a few of the pistols out there that offer easy concealability and are very shootable - with adequate training.
We can recommend pistols all day long (I will recommend that you start with those listed above), but the best answer will come from handling and possibly shooting each pistol that fits your hand well. Many shooting ranges offer rentals that will allow you to get trigger time with prospective purchases, and I believe that type of experience is far better than any advice you could receive from an internet stranger. Stay safe, and happy shooting!

Taurus PT-111 G2 will serve you well. I have XXL hands and it gives me enough "meat" for a comfortable grip yet is highly concealable. 12+1 capacity is a major plus as well.

Taurus 709 slim 9mm. Its only $189 new and incredibly underated. Large grip and trigger gaurd on a very compact 9mm. Incredibly lightweight small gun. Very popular. I shouldn't say underated, the reviews are phenomenal. I own one and it has never misfired once, no failures of any kind. No break in either, just a great gun for a low price.