As a new member who just joined I agree with those above we have gone both routs. Built an IT car then bought an EP prebilt car built car was much fasted and sorted. You can do what you want and build a car if you have access to a lot of tools and have a lot of friend in the fabrication/machinging world, and do it for a relatively low budget. It will take a lot of time though, the first thing will as stated above plan on what you want that will fit in your budget, then start crusing the net, the are a lot of good used parts out there for at least 1/2 of what it would cost to buy new. Secondly look for a parts/basket case race cars lot of good stuff, also dont forget that a lot of 510 stuff will fit the Z. I have seen a lot of people selling old 510 race cars less motors fairly cheaply You may be able to get parts off of them.
As far as the diff if your are planning on running a near stock motor forget the R200 its very heavy and would be overkill, the R160s will work (we ran one for years in our 240 autocross car.) The are light and dependable, most importantly cheaper than R180s or 200s, also the Subaru R160s came with LSDS the old ones esp. are cheap I have seen then for as little as 100 used, so even if the broke you could afford to replace it cheaply, also this allows for a grater selection of gear ratios,if not that then just run a welded R180 again lot to be had cheap and for a beginner locked vs LSD wont be a big diff, for brakes either run the 280zx conversion or the Toyota fronts with zx or 240sx rears you can scrounge these from junk yards for little or no cost then get a good set of pad, if you can fab brackets and hardware and do you own welding you will be able to come close to your budget of 10K, that being said if you dont have access to inexpensive fabrications your cost will go out of sight quickly, even if you do find used parts cheaply. Also depending on what part of the county you are from will have an impact on your cost (west coast is a lot more expensive).
Look at the racing forums there are a lot of good used racing parts there (NASA, SCCA , IT ,PRODracing, ect.)esp thing like seats insterments belts ect. Another cost is lighter bodywork nothing helps a race car mors then less weight so you will want to pull everything off you can get, so fiberglass body pannels plus lighter wheels will be a must depending on what direction you are planning on going (for IT the car must remain mostly stock).
Also agree with those who stated building toward a set of rules you think you might like to race in the future, so you dont end up investing in say a set of trick shocks that you later find out are not legal for the class you want to run somtime in the future,that is where looking at the different orginazations and the rules for the cars will help you decide which direction to go.
Good luck though love to see the old Zs out racing still.