Spindoctor, there are lots of good points above already but as I'm 50-60% through this build process myself I thought I'd give you a few comments.
You say "what in your opion would be the best car for me to use for this build.", but this is something really only you can decide on. Do your homework (which you're clearly starting to do) and decide for yourself. Don't go to great lengths and expense to build yourself a car based on other people's opinion. There are plenty of really friendly people in the Z community who I'm sure would give you a passenger ride in their cars so you can see for yourself what the options are. With a bit of research you'll soon work out what the best option for you is based on what you want to achieve.
With my build I wanted to have something which looks fairly classic on the outside but with modern, reliable engine & running gear on the inside. I also wanted to use as many modernish parts as possible so that I could replace them easily when needed. I also wanted the power to be scaleable in case I wanted more in the future and I prefer the characteristics of a turbo engine over N/A. I don't intend to compete in any motorsport and I want the car to essentially look like a classic but feel and drive like a modern supercar.
With that as my starting point I had two obvious potential donors: Skyline or Supra.
This really translates into 3 main engine options: 2JZ, RB26 or RB25.
I was really tempted to go with a 2JZ but I wanted to mainly use Nissan parts to keep closer to the Datsun lineage. Whilst the RB25 makes a great donor, I went RB26 to account for the scaleability I wanted whilst maintaining a good level of all round usability as per johnymd's suggestion.
There are loads of other engine options. No one is "better" than another really, it just depends on your aims, budget and competencies.
Based on my choice of engine, here is a list of parts you'll need in order to do a similar build:
RB26/RB25 engine. (Mine is a 26 from a late R34).
RB25 gearbox. (RB26 gearbox is 4WD and won't work)
Custom/modified sump. (Neither engine has a sump that doesn't hit the subframe/steering rack. Off the shelf items are available from the States but are really expensive.)
Custom/modified prop. (The new prop needs to be the right length for your diff/gearbox choice. Off the shelf items are available from the States but are really expensive. If you can spec your own you can get them made for a good price in the UK.)
Custom exhaust. (Off the shelf components exist but again are expensive.)
Custom engine mounts. (Off the shelf components exist but again are expensive - see Wyn's link.)
Engine loom.
Fuel pump. (Lots of options here.)
That's really just the start. Here are a list of things I've done in addition:
Brake upgrade. (transferring the Brembos from my donor skyline. They're huge and there's really good parts availability for them.)
All suspension components upgraded and replaced. (Largely going T3, some custom).
BMW power steering conversion. (PAS is something which is much argued over on Z forums but again, make your own mind up.)
Skyline LSD conversion.
Uprated driveshafts.
Custom machined front hubs. (Allow fitment of standard Skyline brake components for better part option and availability).
Chassis strengthening (The standard frame rails aren't full length, nor tie into the rear end).
These are just the first things that spring to mind, there are easily more to consider.
Another question is "what can you swap from the donor car and what donor cars are available?".
I have just finished stripping my donor for parts so can tell you what you can swap. I had an R33 GTR with an R34 GTR engine already installed.
R33's are, at present, the cheapest option. R32's are becoming more sought after as classics and R34s are yet to depreciate to the same level as 33s.
Here's the parts list I took from the Skyline:
Rear driveshafts.
Rear 5-lug hubs, wheel bearings and handbrake assembly.
Rear brake discs & calipers.
Rear diff.
Front discs & calipers.
Engine.
Engine loom.
Fuel pump.
Bear in mind that none of this will bolt straight in and custom parts/work will be required to use them.
I've taken a few other parts which I'm also working on fitting into the 240 although have yet to complete, largely the aircon and automatic climate control system although this is quite challenging to fit due to space constraints. I'm also hoping to use the heater blower and wiper motor due to better performance and parts availability.
It's worth adding up the price of the parts you want to use vs the cost of buying a donor car. I bought a donor car because I was initially worried about the wiring and because I got a really good deal. Subsequently though I would be reasonably confident I could make most of the wiring from scratch and am thinking I probably will just make completely new looms for the whole car.
LHD to RHD
I'm really glad I bought a US shell. It's in astonishingly good condition for a '71 car. It was ziebart'd from new so even the inside of all the chassis rails and wheel arches are near enough perfect.
There is already a recent thread running on this site regarding the parts list needed to do the RHD swap so I won't go over it again. That said though, I'm halfway through making a solution to this which I think most people will find preferable to the conventional swap. I'll document it on my blog once I've finished and know it works.
Cost
Take whatever you've got in your head and at least double it. It would be possible to do the whole thing on a budget but the car you'd end up with would be quite different. I think it would have been cheaper for me to buy a mid range BMW and drive around throwing £20 notes out the window then it would be to complete this build. The point is that before you spend all that time and money, just be really sure you're building the car you want.
I have my own lathe, mill, welding gear and other workshop equipment. Don't underestimate how much custom work needs doing and how much it costs if you can't do it all yourself.
I also have a friend who's been really helpful and supplied me with a lot of the Datsun parts I've needed. Without him I'd probably still be looking for a lot of them. Don't underestimate how long it takes just to acquire all the parts you need either.
In spite of all the obstacles above, I can say that the whole build hasn't been particularly difficult and the end product should (hopefully!) be pretty awesome! I've tried to give you the benefit of many hours of research which is possibly the most time consuming part. There are quite a few people on this forum who have completed their hybrid builds who will probably be better placed to advise you than me but I'm happy to help answer any questions where I can.