A) I have yet to see a 3d printer with that large of a build volume (even as a kit) cost under $500.00.
B) See "A" - when all is said and done, you will be spending $500.00 and more - kit or not. Especially if you want accuracy. You don't say what kind of accuracy, but if you wanted excellent accuracy, it would mean purchasing ball-screw linear motion drives (ball-screws, anti-backlash nuts to fit, couplers, steppers, bearings, etc), with likely similar ball-bearing linear slides. Ultimately - all of that alone will likely eat up $500.00 or close to it.
C) You can have both - but it would take multi-start ball-screw drives (and nuts, etc), and fast steppers.
All of that said, about the only way you are going to be able to do what you want to do - is to DIY (not from a kit) - stick with belt drives (similar to a standard RepRap or Makerbot) for X/Y - and an acme screw drive for the Z axis. Keep the Z axis separate from the X/Y axes. Find a cheap source of steppers/belts/etc (do more research here). There are a few people on Ebay selling large (15 - 18") printer carriage linear stages - they usually include a stepper, belt, and a linear carriage, along with drive and idler sprockets. Not the greatest in accuracy - but they are cheap (about $20 - 25.00 each). They could serve as a start.
Purchase your extruder and hot-end - you'll likely not be able to easily do better homebrew. Get familiar with the terminology - if you want better accuracy, reduce the weight of the hot-end - an off-board Wade-style extruder will allow you to do this, but it has its own pitfalls...
Consider building a RepStrap device first - and use it to build the parts for your 3D printer.
For a frame on a budget - Home Depot aluminum extrusions are fairly inexpensive and easy to work with using a hacksaw and power drill. Just make sure to keep everything square. Also - for the "square" part of things - look into "gridbeam construction" to get some ideas. Or - look into 80/20 extrusions (also known generically as t-slot extrusions). More expensive than other methods, but they can make up for it in ease of assembly and accuracy.
Find a local makerspace if you have one - they may be able to help you with things (be sure to support them with a membership!) - you might be able to get access to 3D printers and maybe other tools (laser cutter, CNC machines, etc) depending on the group. Worst case, you'll be able to get local advice from people interested in these things, just like yourself.
Old printers and flatbed scanners have a wealth of parts in them which can be useful for DIY 3D printers. Just another source option I thought I would throw in...
Good luck! 