Help me pick my next gun

[Colt46]

Pretty much the ultimate nine.

[BingoFuel]

That's a healthy budget you have there and it would be a pleasure to aid you in spending it.
The question you have to ask is what operating system you want to run and from that, what type, brand and model of gun you would like to purchase. In the case of semi-auto that would be DA only, SA only, or DA/SA. I'll use the first two terms loosely but will try to break it down simply.
DA/SA covers the category of (most always) hammer-fired guns that operate differently on the first trigger pull then subsequent trigger pulls. Unlike SA-only, they don't have to be cocked to fire the first round but the first trigger pull is substantially heavier than the subsequent ones since the first pull is both cocking and releasing the fire control system. The problem here is that it is difficult to be equally accurate with the first firing and subsequent firing when the trigger pulls are so different. There are ways around this, but it is a fundamental feature of the design. Great handguns such as many CZ's, all H&K's and most (all?) Sigs are DA/SA operate this way.
SA-only is characterized by having to cock the hammer before first firing and then the gun is is cocked after each firing. The 1911 is of this design. It leads to a great light trigger action but does require that first cocking (or carrying it cocked and locked) before getting off the first round.
DA-only comprise the vast majority of striker fired guns. Every trigger pull is the same weight including the first one. There is no apparent cocking of the gun, though that is conceptually being accomplished as you begin to pull the trigger. The mass market of Glocks, M&P semi's, XD's and many others all work this way.
I've been an H&K fan for years but have now decided to move away from a DA/SA design and move to striker fired DA-only models such as a Glock or a M&P. In fact these DA/striker fired guns are often less costly than quality DA/SA guns such as H&K and Sigs. I'd recommend just buying a Glock or M&P here which will leave enough money for a:
Revolver. Two types really. Again DA/SA or SA only. The DA/SA revolvers have the same apparent operation as the DA/SA semi-autos above. That is, a heavy trigger pull the first round and then light trigger pulls for subsequent rounds - that is, until the gun is emptied or decocked. Like the semi-autos, in many cases that first heavy trigger pull can be circumvented by manually cocking the gun. The majority of S&W .44, .357 and others (629, 626, etc.), Rugers and others operate this way.
Alternatively there are SA-only revolvers which require you to manually cock the gun prior to each round fired. I have no hands-on experience with these guns but Ruger and a number of others still make them. Used for cowboy action shooting and range and woods use as well.
I'm a Smith and Wesson fan here and depending on your planned use, your hand size and your ability to cope with recoil, you cannot go wrong with one of their Performance Center DA/SA revolvers. I have a V-Comp in .357 and .44 respectively and they are excellent. Or one of the new Classic series would be outstanding. But these things are pricey. Plan to spend between $700 and $1500 for these fine handguns. Or you could stretch your budget and look for a lightly used Colt Python which is, for many, the top of the list of well made and beautiful revolvers.
Before there is a lot of bash headed my way, I tried to accomplish a few things here:
I played loosely with the detail behind these designs to convey the salient points in choosing a next handgun. As such please excuse the muddying of some of the definitions all designed though to make a point;
I tried to lay out the info to set some context for the decision making. Trying to compare a CZ to a Glock to a 629 and claiming one is 'better' when they are so completely 'different' is just confusing.
Or said differently, just buy a S&W PC V-Comp in .357 because it's better than a Glock or a Sig
B