I think Dolfan's advice was very good.
One additional thing to consider is whether you are mechanically inclined and want to learn to tinker with the car or not. If you want to learn to tinker, get a carburetted motor.
You will want to upgrade the ignition - I see a lot of people here use MSD distributors and boxes. I have a pertronix in my car and it works great with the stock coil, but my car isn't high performance. You'll need to upgrade the cooling system as well - I'd recommend a generic aluminum radiator, whatever fits.
I won't try to top the above recommendations - except to say that if you're putting a lot of miles on the stroker will wear out sooner. If it's a 1,000 mile a year car - stroking a 302 to 347 shouldn't be a problem for reliability. Also, a stroker has more torque but won't want to rev as high - consider what you prefer. If you are putting very little mileage on it, you could probably just have a shop tune it up every spring and you would have very few problems with a carbureted motor.
If you want the thing to start easily the first time every time, no problems re-starting it on a hot day, hands-off mechanically.. I recommend you go with a 5 liter EFI motor. It will be more expensive, but you won't have to mess with it. Some of Dolfan's suggestions still apply (heads, headers, ARP bolts). However, I think you should set the car up for a supercharger (lower compression pistons, blower cam). A blown EFI motor should be very reliable, and make your power goals easily without revving sky-high. It will have a lot of torque as well.
For the transmission, if you prefer an auto - go with what Dolfan said. If you want a manual, go with a Tremec 5 or 6 speed and have a hydraulic clutch installed. It may be difficult to make budget while converting to a manual trans, so if you can live with an auto you may have to. I personally would settle for less horsepower and get the manual trans, but I don't know what your preferences are.
You said that the $10k was for engine/trans. Keep in mind that the driveshaft, rear end and rear suspension will have to be upgraded as well when you put this motor in.
My last suggestion you've probably already started. You'll want to contact a few local custom shops / engine builders with your ideas and get their recommendations and estimates. Hopefully you'll find a place that's done similar work in the past and will let you talk to past customers.
Sorry no links, just general advice. If you're having someone else do the work, they can take care of the details. That's where the budget can easily get blown, or not.
Good luck, it should be fun!
