I switched about a year ago, and got a 6-inch Lumia 1520. Never looked back.
Amazing screen, amazing camera, battery lasts for 2 days at least with constant wi-fi, gps and moderate usage. Interface took some getting used to, but now i swear by live tiles - they are just THAT informative. Regarding app gap - it shrinked substantionally since WP was upgraded to 8.1 (i have about 400 apps in my store history, but i obviously don't use all of them). WP8 also has a good updates history, and it's pretty sure that all current phones (lumia ones at least) will be getting the universal OS Win10 (which is looking to be a beastly thing).
In a nutshell: WP8.1 - 10/10, would bang.
Edit:
As someone noticed - to get the full experience you should aim for a top of the line models, like 930 or 1520 (only major difference is size and microSD in 1520). But one would think it's self-explanatory.
Edit2:
If in US - do not, whatever you do, get a carrier locked Lumia. I don't know about lesser models, but i've read that AT&T 1520 missed tons of features compared to a unlocked one.
Edit3:
In your price range i'd check out the 830. It's not the flagship, but i'd say it's upper-mid tier in Lumia line.