What would be the ideal engine if I were looking to build a very fast 65 Belvedere.  A 426 hemi?  Would a 500 wedge work?  Looking for opinions.  Can't spend much more than $15,000 for the project.  

15,000 bucks, lets see, have you done any suspension mods? What kind of tranny work and torque converter do you have? Have you put disc brakes on that thing yet to slow it down? What size of gears and what rearend is in that car? Is this car tubbed or does it have a roll cage? Is it a race car or a steet car? Do you drive it everyday? How many miles do you drive it every day? On the street, on the highway. The ideal is economic's. A nice set of wheels and tires could run you 1500 to 2000 bucks. A built 727 could run you 1000 bucks with some goodies in it. A good torque converter could run 600 to 1,000 bucks. If it's a 4-speed, has it been rebuilt lately? A good clutch could run you 450.00. Do you know how and have the garage to do alot of your own work? Can you rebuild a 727? Rebuild a suspension? Do you have a shop with a lot of tools? What do you consider very fast? How much horsepower do you think is enough? 15,000 thou sounds like alot, but really, you could build just the short block for that, meaning Keith Black! Or you could have a Kobelco high helix screw-type supercharger for 15,000. How fast do you want to go? I think it would be best to come up with a plan on the whole car. I spent 2500 on just my paint job. 15,000 will go real fast on nickel and dime stuff. Let us know. You could have a healthy 440 that could get you in the elevens if thats what you want and still have money to spend on other stuff.

if you already have a trans conyertor and a good car suspension wise . my 65 belvedere went 8.60s in a quarter on a 150 hit of nitrous with a 55 inch b-1 headed motor i had right around 15000 in the motor if you have plan its not that bad you need to research different combinations and stick to it. if your wanting 11s or a high 10 that can be had easily for alot less money  

Building a VERY fast car for around $15,000 can be done, depending on what you call VERY fast. Money goes away quick if you don't have much to start with.

What do have so far, and what do you call VERY quick?  

I would recommend starting out slow and working your way faster, its all about the combination so here goes, Best Bang for the buck? Simple, 400 block with 440 crank equals 451, install ported polished 452 heads with 2.14/1.81 valves.
Torqer Intake or similar, 850 double pumper, 3800/4000 stall dynamic 9 1/2 in converter, turbo action manual valve body with a good rachet shifter, Hurst Pro rachet 2, or B&M quick silver.
solid cam, mopar .528 or .557, will do nicely for an 11 second car.
Go .590+ cam for 10 second car.
10 to 1 compression for 11 second car.
11.0/11.5 to 1 for 10 second car.
Keep the rotating internals as light as possible rods, pistons, crank.
Round off the package with a 4.10/4.30 gear.
Stuff the biggest tire you can in the wheel wells, please don't cut them. I currently run a 67 Satellite with a 28x10 Mickey Thompson D.O.T. with a 15x8 weld, I just had to remove the inner lip of the fender to make them fit. These tires have a section width of 12.5", I have had 29.5x10 M.T. with tubes installed, stuffed in there with slight rubbing going around corners.
Cage is obvious, always try and reduce the weight, glass, fenders/hood, of course this will depend on your budget.
Good bang for the money, light weight aluminum wheels.
Welds are some of the best value.
Might want to upgrade your 40+ year old axles if your planning on going fast.
9 seconds you say, roller cam, 750 lift, 12.5 compression, 1050/1150 dominator, Wheel Tubs 14x32 slicks, 45/4800 converter.
Trans. brake, Trans. blanket once your running 10's.
Good Luck its all fun just stay safe and plan out your combination from the beginning, that way you may only have to spend the money once.  

Can you do the work yourself? This is very important. Shop for the best deals,find reputable machine shop, spend your money wisely, do your homework, don't be afraid to ask for help. You can build an 11 sec wedge motor( no NOS) for less than $5000 with aluminum heads. You can still buy BB from a junk yard. You will not find a Hemi in the junk yard. Don't forget all the other stuff, trans, suspension, gear, tires, car, body work, paint, etc,etc,etc. Its not just the cost of the motor, and $15,000 spent only on motor will not make the car run 11's.  

I think the key is how much can you do yourself ?