I think you can decompose this pretty quickly. You've already picked a caliber, so you're most of the way there
With the "no external safety" guideline, you pretty much eliminate 1911s. Arguably anything with a grip safety, like Springfield XD, although I'd make the case that it's disengaged just by holding the gun properly and therefore does not count as an external safety that requires any extra steps (like a thumb safety, for instance).
If this is a do-it-all sort of gun for range/home defense use, then you probably want a double stack full-ish size pistol with at least 15 round capacity.
1. Do you ever intend to carry this concealed? If no, you may as well go big or go home and get something full size (Glock 17 is a good representative of that, or a Sig P226 or Beretta 92fs). Big, hefty, easy to shoot and control.
2. Do you want a consistent trigger pull? If yes, then most likely you want to stick to striker fired guns. They all have the same trigger pull from one shot to the next. Generally not as light and crisp as single action hammer guns (at least in stock form) but also far lighter than double action hammer guns. I happen to have come around to a preference for hammer-fired, DA/SA on a carry gun, but unless you have some real pressing reason for it, you can probably stick to striker fired.
3. Another angle...if there's no limit here, then do you want something with more value than just reliability and utility? Something iconic, or something with "personality?" Glocks and the like will run forever, but they're all pretty boring (that's why they run forever!). Do you want something like a Beretta 92, or Sig P226, maybe CZ-75? These may or may not have external safeties (they will at least have external decockers), but there's something about them that's just so much more interesting than modern, black, plain-Jane striker guns. Go hold an all metal, highly polished Sig P226 with Rosewood grips and tell me it isn't sweeter than a reliable piece of plastic
That Sig may set you back $1200 or more, too. How much value do you put on the awesome factor?
So having considered all that, most likely, you'll want to get a modern striker-fired 9mm handgun in either full size or "compact" size. Again, reference Glock 17 and 19 as size standards. I'd probably advise people toward the 19 size because it's darn near the same as the bigger one, but more easily concealed. At least you keep the option, and you can use extended magazines in all of them. Thus, here's my list (worth every cent you've paid for it) based on 100% subjective impressions I've gained over the last year. Note: I put a lot of weight (no pun intended!) on trigger pull and ergonomics/comfort. Some guns just point naturally for me, and others seem not to. It will be entirely different for someone with different hands, height, eyes, etc.
1. Walther PPQ: about Glock 19 size, fantastic ergonomics, and a trigger that really is awesome. It feels very much like a Beretta 92 trigger in single action, maybe *just* heavier, and the reset is unmistakable. I own this in the 5" barrel for range and competition use. I can hit targets and make follow up shots faster with this gun than any other I've used. I even got it in .22 for more practice at less cost. Decent aftermarket support.
2. S&W M&P 2.0 (and compact): the super rough grip texture is a love-it-or-hate-it kind of thing, but you can cover it with something if it bothers you. I thought this was a huge improvement over the first generation, and the trigger is now quite nice too. This one just fits my hand wonderfully. Good aftermarket support.
3. Sig P320 (full and compact): Was my #2 until I found I shot better with the M&P 2.0. Very similar in size and ergonomics to the M&P also, and with a very crisp trigger. Read about the modular/interchangeable parts...not a useful feature for me, but maybe for you. It's a flexible platform. Shoots great, runs great. Feels kind of top-heavy to me. Decent and growing aftermarket support. It's the Army's new sidearm for a reason. It's really good.
4. Glock 17/19 (Gen 5): I like both. Glocks just don't "fit" me well. I don't know why. There's nothing wrong with them, I just have a natural preference for the others on the list. Glock is synonymous with aftermarket and you can find everything you'd ever imagined to trick it out. And there's a certain icon status to it, too. It pretty much created the striker-fired market and still dominates. I happen to think the guns above have out-Glocked the Glock, but again that's all subjective!
5. Ruger American Pistol: I actually like this gun. It doesn't get much love. It's heavy and built like a tank. I'm not sure how many people really even own one, but I found it very easy to control and to be accurate with. The ergonomics are pretty good, as is the trigger.
There are of course many others. I'll say I owned a Springfield XD Mod.2 for a year and recently sold it...reliable and with good ergonomics, but I just found that I liked other models much better. This one has a grip safety. Also, I have not had a chance to try Beretta's new APX, though it feels nice in the hand and looks a little funny. Way too soon to know whether this will become a real player, or just fizzle.
Oh, I also tried a CZ P10c. As much as I like CZ, and for as much good press as that gun has received, I just plain didn't like it. I can't really say why!