For your budget I would get a cz 75 sp01. If your looking to save some money the p09 will do and you can find them from Kentucky gun co. For 442$ free shipping. Factor in a 20-30$ charge for a transfer and it's about 475$.
Given your willing to spend 800 though I would get an sp01.
I'm about to pick up a p09 in 40 and a p07 in 9mm. If they would just make a safety variant for the sp01 in 40 I'd probably be going that route. But I'll have more cz's in my future. The new polymer series are probably the best all around gun for the money in the polymer class. Accurate as hell maybe the most accurate polymer gun I've seen and just as reliable as the others. Yet nearly 100-150$ cheaper than the glocks and M&Ps. Or at least their cheaper than mine. I paid 550$ for my M&P and 650$ for my glock. Both straight up retail
Gotta jump on with the CZ P07 recommendations. It certainly meets all of your stated criteria. It is also a good option for concealed carry, so it can do double duty, if needed.
The stock P-07/P-09 is excellent its own right and an outright steal at $450 + FFL fee, but if your budget is $800, that puts you in range of a fully Cajunized model from Cajun Gun Works ($700 + delivery & FFL).
This is only based on initial impressions of both ergonomics And DA/SA triggers: the CZ-75 stands out, and were I seeking a first handgun in 9mm Luger, it would be the CZ-75 Compact.
All of my handguns are compacts, and this version of the 75 would be easier to legally conceal.
The full-size 75's trigger had even better engineering than my CZ-82 (in 9x18), but although I' ve not seen a Compact....that is my type.
For full size 9mm HD I would go with a Walther P99 or PPQ, they are son to release the PPQ in .45 as well. I love my Walther PPS, my concealed carry edc pistol. FN FNX are great also. I want one in .45
For the P2000 vs USP, yeah there is still reason to get a USP. There are more Variants, and some people prefer the option to carry with the hammer back and weapon on safe. Safeties were not available on the P2000 or P2000sk, although HK has brought them back to the P30sk and such. I thought the safety would push me towards the USPc, but I couldn't pass on a deal for a P2000sk DA/SA and I couldn't be happier.
For the next 9mm, I'd say something in the CZ line for what you're asking.
If it were me I would bump the cash up a bit to $850 OTD and get a Sphinx SDP Compact. It is a cut above other guns in its price point. It is better out of the box than any Sig I have ever owned and better than the HKs I have bought and then sold over the years.
It is IMHO worth double what the P07 is worth. They are better than the Pro-Grade P-07 from Cajun Gun Works. Nothing in the price range is equal IMHO in terms of parts quality, machining, fit and finish. It is s few minor tweaks away from being 9mm greatness.
Stoeger Cougar is a good option, essentially a Beretta for 2/3 the price. Also, SAR's ST10 is worth a look. Both made in Turkey, and very good guns for the money.