Goldfish:
This is hopefully semi-coherent. If it reads like Greek please let me know! I'm trying to capture all my thoughts at once while trying to answer your questions so it might not be very coherent.
About HD, HDV, resolution and HDTVs:
ALL versions of HD are 16:9! Don't listen to anyone who tells you HD is 4:3!
The high definition spec requires specific frame sizes of 1920x1080 and 1280x720. Those are the *only* pixel counts that can be considered "HD" for use on a home system (pro HD cinema cameras are a different story as they are not restricted to HDTV requirements).
1920x1080 is often refered to as 1080p/i and 1280x720 is refered to as 720p/i. Each of these can have progressive frames or interlaced "frames." Progressive frames are full frames scanned from the CCD(s) - precisely the way film is. Interlaced footage is composed of two fields (for historical reasons) that are each half resolution and both are played together to create a full frame. This is, however, not without its disadvantages. Interlaced footage displays each field separated by a small time interval (historically this was necessary as TVs could not scan an image fast enough resulting in the image dissipating towards the top of the screen before the next frame was scanned). This is the largest contributer to the "video look." Because of have 60 different fields being played rather than 24 or 30 frames you get a much much smoother motion rendering resulting in "hyper-realistic footage."
the High Definition spec allows for:
1920x1080 interlaced
1920x1080 24 progressive
1920x1080 30 progressive
1280x720 60 progressive
1280x720 30 progressive
1280x720 60 interlaced
1280x720 24 progressive
Because of the smaller frame size 720 footage can increase the possible progressive framerate while staying without broadcasting bandwidth limits.
What does this matter for our discussion?
The JVC creates 1280x720 30 progressive frames per second
The Sony Creates 1920x1080 60 interlaced fields per second
30 progressive frames cannot be transfered to film and look good. 60 interlaced does much better. If you want to "go to film" then the Sony is what you are looking for. If, however, you can do without 24 frames per second footage and want a look close to film the JVC is the better choice. The DVX shoots only standard definition 720x480 but shoots in true 24 progressive, 30 progressive and 60 interlaced modes.
*Please note that both the JVC and Sony fit the high definition specifications. They are just different forms. Both should look great on a large screen.
Progressive footage in NOT line doubling! Line doubling refers to a feature of HDTVs which upresses (increase the resolution) of lower resolution footage so it can play on an HDTV. Progressive scan is a full frame scan of the CCD (image sensor). Hence the reason it looks more like film (as film is a sequence of whole frames).
Interlaced footage can be rendered to progressive footage. This is often called "deinterlacing" as you are combining 2 interlaced fields into one full frame. There is some great software out there that will do this wonderfully.
So where does 1440x1080 come from? Well the current Sony model only captures 1440x1080 and then converts this, in camera, to 1920x1280. Thus your final image will be 1920x1080 but the amount of actual data captured will representative of a 1440x1080 image.
All the professional HD cameras I am aware of use a single chip so you can get good footage from this set up. The difference is that these are usually _large_ chips and not the 1/3" chips you will find in either of the "prosumer" HDV cameras. In general 3 chips will produce much better color. With one chip each set of four pixels records a separate color - two green, one blue and one red. The problem with having each pixel capture a color is that you effectively mutilate the amount of color data you could have. With a 3 chip camera you have a separate chip for each color. Each of these three images are then combined to create the final product.
Vegas will edit high definition footage. It will use a lossless compression (ie just manages the data better, you don't loose anything) to allow faster editing but that's it.
The guy was right about one thing though. Not very many HDTVs will play true 1920x1080 footage. It is usually downconverted slightly. Plasma TVs will display the full 1920x1080 image unmanipulated. It sounds like what you are looking at is a projector with a separate screen? If so check the projector and see what it is capable of displaying. It should say in the specs.
So bringing it all together.
The JVC does 1280x720 30p
The Sony does 1920x1080 60i
The DVX does 720x480 24p, 30p, 60i.
If you want to project this onto a wall the HDV cameras will hold up better. You CAN "upres" the DVX footage to fit the HD specs. It will hold up well. The DVX will be softer though as you cannot create more detail in the image just blow it up so it does not pixilate. The HDV cameras will be MUCH more detailed.
The Panasonic MAY have a better lense. It certainly is better, IMO, than the JVCs. The Sony however has a lense designed by a very high quality lens crafter... only time will tell how good it is.
Hope this made some sense. With all of the round about discussion I think I may have made myself sick trying to read it!

Please ask questions if you have any!