Definitely go shoot a bunch of different handguns and see which one fits your hand best, feels the best to you, is the right size and thickness, and has other features you like.
I just bought my concealed gun about a month ago. Ended up gettin a Springfield XDM 9mm 3.8 compact. I shot a Glock 19 and 23, the XDM, Beretta, Ruger, and a Kahr and i liked the feel of the XDM the best. The only thing I wasnt a huge fan of was the break point of the trigger which I replaced aftermarket for a trigger that breaks much earlier like a Glock trigger does.
Another thing to consider is single or double stack mag. You can get a really really skinny gun with single stack mags like the XDS for example. I prefer the double stack just because it cant hurt to have 14 rounds in a compact gun or 20 with the extended mag. Again personal preference.
Weight is another big issue. Most compact guns now days are polymer frame with a steel slide to cut down in weight. They all weigh within a few ounces of each other. But if you do decide to go for a full metal gun, its going to get heavy after lugging it around for a while in your waistband.
Last thing is striker fired vs hammer fired. Striker fired guns tend to have shorter slides which makes them kick less since your hand is closer to the bore axis. I'm not also big on the whole SA/DA thing or carrying locked and loaded so I didnt need a hammer fired gun.
Just some things to think about and if you have any more questions feel free to PM me.