I am only going to list full size guns as they dont punish the user as bad and will give you a baseline feel to the gun.
SAO Trigger
1911
Hi Power
DA/SA Trigger
226
92FS
CZ75
Striker Fired
G17
M&P9
XD
If you dont like them in their full sizes, your probably not going to like them in their compact versions. All can be carried though.
I agree with the above. Try full sized first.
Decide revolver vs. semi-auto first. Start w/a 4" DA revolver (e.g. S&W Model 10). Don't try a 2" snub nose first. They are much less pleasant to shoot and may prematurely turn you off of revolvers. I have seen this happen before. A 4" revolver is one of my favorite guns to shoot, but a 2" snub nose is quite different. There are also 3" options that split the difference. If possible, you can get a .357 mag so that you have the option of shooting both .38 spl and .357 mag if you so choose.
For semi-autos, decide if you like steel, alloy (aluminum), or polymer frames and striker fired (Glock, XD, etc.) or hammer fired (e.g. 1911, CZ 75). Steel frames (e.g. CZ 75) absorb recoil, but are heavier. Alloy frames are lighter (e.g. CZ P-01 or PCR). Polymer frames are light, as well (e.g. XD, Glock 17).
Once you try full sized, you can try some of the compacts (e.g. Glock 19, CZ PCR), sub-compacts (e.g. Glock 26, CZ 2075 RAMI), and mouse guns (e.g. Kel-Tec P3AT, Ruger LCR, etc.). Of the small guns, I would definitely try the Kahr PM9 or CM9. They are single stack, small, and light. They are easy to carry, but more powerful and easy to shoot than the .380 mouse guns (P3AT and LCR, for example).
Another gun I would take a hard look at if you can find one is the H&K P7. The PSP (not the M8) version is cheaper, and it has no controls to snag. It's a smooth, snag free carry gun with a great safety mechanism (squeeze grip safety). It's a bit on the heavy side, but it's very accurate as it has a fixed barrel (not locked breech like a lot of modern semi-autos over .380 ACP). The fixed barrel design allows a good amount of barrel length for the size of the gun, and the design also makes for a very small slide profile, which is good for carry. It's very easy to field strip, as well. With a good holster, the P7 is a great option. It also satisfies most crazy gun control law capacity limits as it's 8+1 capacity single stack.
Decide if you like manual safeties (i.e. something you have to remember to flip off when the SHTF, so you have to practice until it's instinctive) or whether you like decockers or no external safeties (i.e. nothing to worry about but squeezing the trigger if the SHTF).
A lot depends on what kind of clothing you'll be wearing, the temperature, what style of carry you plan on using (pocket, IWB, OWB, shoulder holster, etc.). You will likely eventually get more than one carry gun as a result. It depends on a lot of the factors above.
Caliber is a whole other debate, but I generally suggest 9 mm as a starter b/c ammo is cheaper and usually more plentiful (though not now, obviously). From there you can branch out in calibers.
I'd look at the CZ 75B with the Kadet .22 conversion kit. The CZ 75B is completely solid and I have heard good things about the Kadet kit, though I do not own the Kadet kit, I do own the CZ 75 BD which replaces the thumb safety with a decocker.
Great suggestion. Then you use the same frame, grip, and trigger to practice. Both are deadly accurate, great guns. Probably hard to use as your first carry gun until you get used to how to conceal a full sized gun, though. You could go the CZ PCR route (shorter barrel & slide, lighter frame). Realistically, I don't think a carry gun needs a rail. That's why I say PCR over P-01. Smoother, narrower contour and no rail to snag your clothing.
The first time you carry, you will feel very awkward and think everyone notices your gun, but they don't. As you get more used to it, it becomes incredibly easy. Definitely invest in a good holster, though. Worth its weight in gold.