Well first off, it really isn't necessary to dump 1K into one car to make it race ready. I would say $500 is alittle closer. Maybe $700 if you have to buy a starter box and radio gear ( which answers one of your questions, bump start is best ).
As with any car, tires will determine how well a car will handle. It has been said many times that with the right set of tires, any car can go fast and handle like a dream. If you're not running them now, foam tires is the only way to go.
If you're looking to get a new car that's fast right out the box, check out the R40 from HPI. If you read thru the R40 thread you will see several people saying it is good in its' stock form. I have one and I agree. And as of right now, I have no plans to add hop-ups. I don't see any need for it.
As for the engine, that's a tough question. I prefer Nova-Rossi based engines. They are easy to tune and run forever. Right now I have a Sirio .12 in my car. That sucker is fast but very sensitive to carb adjustments. I would not recommend it to any new comers. Stick with a Nova-Rossi engine and you'll be happy.
Good Luck...