Opinion?
Keep your money for the moment. I appreciate that you've saved a fair bit for your motor, and roughly the right amount. But:
1. You're new to cars - you said yourself that you don't know much about them. You're talking about an automotive heart transplant - even if the engine was designed for the car, there's still complications (just like putting my heart into your chest). If you're not comfortable enough to do the swap yourself, you won't be comfortable enough to fix it.
2. If something goes wrong, you're screwed. You're reliant on the person who performed the swap to fix the problem, at his/her convienience, and more importantly, his/her price.
3. While engine swaps are fun and grand things to do, there's lots of other things that can be done to the car. Not even counting the obvious (wheels/body), what about brake upgrades (my stock S13 brakes blow - switching to the Z32 (that's a 300ZX) brakes is a good project for someone who wants to get into it)) or suspension upgrades (lowering the car for increased handling, tunable shocks for better ride, strut tower braces (that's the bar that goes across the engine bay) to stiffen the chassis (less flex = more stick), etc)?
4. Driver training. I have no idea how old you are, how skilled or experienced you are, or anything else, so please don't take this as an insult. The single best modification to any car is a better driver. What good is power and handling if you can't use it?
Then there's the stuff nobody thinks about, like rollcages, race seats, 4 or 5pt harnesses, and other safety gear.
Tips for gettings started - MONEY:
#1 TIRES - The four most important pieces on your car - everything the engine and suspension do must go through these tiny patches of rubber to get to the ground. Burning out never made anyone faster, and spinning never made anyone take a turn quicker. I like the Falken Azenis, Bridgestone Potenza S03 Pole Positions, and for the budget minded, Kuhmo Ecsta Supras.
#2 BRAKES - If you can't stop, that fast car isn't going to do you much good when it's buried in the trailor of a semi. There's the Z32 (that's the chassis code for the 300ZX) swap, and Brembo says they will make a kit (includes rotors/calipers/etc) if ten people order it.
#3 SUSPENSION - Now that you're not plowing in a semi, and you can put your current suspension to good use, time to get a better one.

Look at coilovers (GAB, Tein, and JIC make good sets), which are matched sets of spings, shocks, and adjustable perches so you can adjust your ride height. The Teins actually have a system available called EDFC (Electronic Damper Force Control) that lets you control your shocks from INSIDE the car (too cool). Look into strut tower braces (again, the thing that goes across the top of the engine bay), but don't forget about things like anti-sway bars (they go between the wheels under the car), tie bars, and the all-important bushings (every metal part in a suspension that joins is connected with a rubber donut - one bar has a hole in the end, like the eye of a sewing needle, that the donut goes in, and the other arm goes in the middle of the donut) - the softer the bushing, the softer the ride but the worse the handling and vice versa.
While you're doing that, do this to improve your skill:
Attend your local SCCA events - you can pilot your stock car; all you need is a helmet (they'll loan you one for free), your car, a valid driver's license, and around $15.00US. They'll not only teach you how to drive, but give you the opportunity to practice REAL racing in a controlled, safe, and legal environment.
If you can afford it, attend a driving school like Skip Barber's, Bob Bondurant, or others. It's usually around $1500, but it's worth it.
Read, read, read. There's lots of books on the physics of actual racing (yes, it's physics, but the books generally don't deal much with math), and lots of books on modifying engines. "Boost", by Corky Bell, is an excellent one about turbos, for example.
ASK LOTS OF QUESTIONS - you can ask me, Daunt, or any of the other "distinguished' members of the board. I have no problem telling you I have no clue when I have no clue.
All in all, welcome to the club, enjoy yourself, and remember - race safe.
