You still haven't mentioned much about your embedded platform. We have no idea what the MCU is or what it can do, what resources are available, or much of anything to make a good recommendation.
So you're looking for:
-a large-ish display (4" to 7")
-a high quality display
-touch
-something where someone did 99% of the necessary work for you ("software library support", not just schematics, datasheets and such)
I think, solutions up to 20$ was perfect for us
-and on a $20 budget (!!!)
You'll quickly find that *nothing* exists that fits these criteria. You have several options that actually exist:
-There's super cheap LCDs that are small and not so good (with the the usual ilitek, solomon systech, sitronix, etc) and mainly with community support. Here we're talking like < $10, 2.x", and resolutions around 320x240, and again, so-so quality. Libraries? You'll find arduino stuff all over the web if that's your thing but that's mainly it. There's no real vendor support. Nobody is gonna be really impressed at how those look outside of hobbyist projects...
-There's traditional TFT LCDs, with either a classic parallel RGB or LVDS encoded signal (colors, sync, pixel clock). Your processor will need to have the right interface. Your OS (Linux, Android, WinCE, etc) will typically have everything you need for graphics. Prices are very competitive (SHARP is pricey and doesn't include touch, TIANMA are cheaper and offer touch, but chinese companies like OSD are quite a bit cheaper still). Great resolutions, large sizes, great quality and all (it's what's in most of your electronics like your laptop or LCD monitor) , and for decently cheap. With a MOQ of 1000, you could get something like a 4.3" 480x272 with touch, with a FFC/FPC cable from OSD (TIANMA would be more and can discontinue stuff/be a problem to order; SHARP will cost similar but have no touch so that's extra $). Again, if you don't have the right interface, then this option ceases to exist altogether. If your PCB person isn't really good or if your design sort of sucks (poor PDN/layout/decoupling at certain frequencies), trace impedance isn't well controlled (proper stackup and all), and you're not familiar with controlling EMC (FCC testing) then you're 99.999% likely to fail tests (most likely radiated emissions, on the 3rd harmonic of the pixel clock), possibly still failing after months and several redesigns and kludges (and tens of thousands of $ wasted, project is now late to market, etc)
-Otherwise you're left with solutions where someone did 99.999% of the work for you, like nextion. There's no need to pick an LCD panel, plan your project to have the necessary hardware resources (spare ports of the right type, enough memory for frame buffers, enough flash left for all the heavy graphics, etc) and nobody needs to spend months or years writing graphics code and necessary "other" stuff (like how to store that on some file system and update it later). There's WYSIWYG editors that use built-in libraries. Everything runs on another processor on the LCD's PCB, using it's pixel clock interface/SPI/I2C for LCD panel, touch panel and storage. That adds a fair amount of cost (you're paying for the software development, the extra PCB, processor, memory and all). The 4.3" unit is $45 and the 7" is $75.
You can't have a everything-included solution (both hardware and software) like nextion without paying for the extras.