Having done one and in the process of doing a '65 your main areas are going to be the sheetmetal and interior / trim. As stated, you should really clean it up, not just out. This will allow you to reall access the body, interior, undercarriage and the like. Sorry for the long post but...
Sheetmetal
Being a CA car the rust might not be as extensive as say a northern or midwest car but don't be surprised if you come across it, particularly the trunk floors, braces and extensions. The only areas that don't seem to rust bad on these is the driveshaft hump and the hump over the rear axle. The driver's side floor, rocker & front post areas also see more rust due to the driver getting in / out all the time. The bottoms of the doors usually rot too because of the drain plugs / holes clogging up with debri. That's why you should actually wash it like Blake said, maybe even a pressure wash it. This helps knock the rust off and help determine where leaks could be. This will also give you a chance to find out if you should go to the next step and soda / media-blast the body. Oh, and prepare yourself that after you strip it down you're going to see even more rust than first thought. Getting that roof straight is going to cost. Also not sure if your doing a frame-off but would definitely replace all the body-bushings too.
Trim
Hopefully trim is in good shape. While this stuff is available almost everywhere it's hella expensive to replace, especially the emblems, bezels (& don't have an SS - sheesh). My suggestion is when you and your bros / pops start with this part of the project do it when you're in a good mood, don't rush and if you have to walk away due to frustration DO IT. This is one area where a BFAH-approach is not needed. The trim bends easily but doesn't go back to its original shape as well. Same with glass, it's available by hella expensive.
Suspension/Drivetrain
Rebuild kits for the front end are pretty reasonable and not too difficult to do, as are the rear-end bushings and the like. Just watch out for the coil springs, even if they're wiped they can still come flying out and do you harm!! Bushings, ball joints and these components I would try to get from the local O'Reilys, Auto Zone, Kragens or other parts stores - buying from a catalog can be expensive. Plus, you can usually get the old bushings removed and the new ones pressed in at these places or you can take them to a muffler / brake place. The brakes are not expensive either and you can upgrade to the front to discs rather easily. Conversion kits, depending on type & where you purchase, can run from $500 and up.
Personally, I would retire that inline 6 for a crate motor 350 or check out locals who may have an engine for sale. Damn near any Chevy V8 will fit in that space with hella room to spare. Or maybe a 283/327 to keep with the old-skool theme. I would also go for no less than a 3-spd auto (a TH350 will bolt right in place of the PG that's in it). You may be able to get some cash for the current drivetrain, particularly that PG. If you're planning to terrorize the street with a hot motor I'd think about upgrading the rear-end. It most likely has the 8.2 in there - they can take abuse but aren't really known for being the strongest. Also realize you have a 2-piece driveshaft plan on replacing that center carrier bearing.
Misc
It's hard to tell you what's it going to cost without first seeing the car without the stuff on / in it, as well as what's there and what's missing. This is also going to depend on your skill & comfort level, and your helpers skills.
It's going to cost some cash and yo're never going to be done
Yes, you're definitely going to have to get a job, maybe two, in order to get this project going & to keep it going
A garage would definitely help, at least in storing parts for clean-up / refurb later
Whether you do a rat rod, lowrider (the '61 - '64 look the best IMO), low-rod, build it the way YOU want to build it. It's your car, your money, blood, sweat...
You're never going to be done
By it being a '64 there are tons of parts available, I didn't have this when I built the '66 but more & more the coke-bottle Impalas are getting more parts. I suggest you start looking at the catalogs like
Impala Bob's, National Parts Depot (NPD), Sinclair's
Impala Parts, Year One (HELLA EXPENSIVE), Classic Chevy Muscle, Goodmark and the like. Pick up a Summit and/or Jegs catalog (hell even J.C. Whitney) for the misc stuff too. Most of these catalogs are free and that'll give you an idea of what's available and the cost. I also suggest shopping around for parts, as some places will have regular versus "date-code" parts, especially for hoses, plug wires and things. I've found there aren't any differences between the two except the coding, which I don't care because I'm not a number-matching fanatic. Lastly, start talking to people who have these cars, see where they go to get parts, service. You may be able to get deals on bodywork, paint, parts and supplies.
Keep us posted and good luck.