Hi Baddy,
Ya I would agree, you did run out and grab a car without doing your homework. But this is sometimes not a problem it just depends on the person, Actually this is how I get into a lot of my hobbies, buying part by part as I learn.
You have quite a few LARGE questions here, so what i suggest is that we handle each question one by one. I suggest we start with your number one, discuss that then move on once everyone feels comfortable. Lets keep this all in the same thread and that way it can be informative for future members.
At the same time Baddy I suggest you do some searches and read on your own.
With that said...ENGINE!
1. The engine choice is really easy in my opinion.
http://www2.towerhobbies.com/cgi-bin...?&I=LXUU27&P=7
This is the Standard short crank version which is what you need for the RC10GT. This is also whithin your price range.
Now, if you purchase ths engine (non pullstart) then you will need a starter box and a battery like this:
http://www2.towerhobbies.com/cgi-bin...?&I=LXAXU2&P=7
This starter box comes with a 12v battery and will also run a wired glow heater:
http://www2.towerhobbies.com/cgi-bin...?&I=LXUC32&P=7
This is what starts the car.
The only other thing you will need is a charger for the 12 volt battery.
Look it up on Tower Hobbies website.
Now on the other side You could go with a pullstart, which is a self contained recoil starter bolted onto the side of the engine.
This eliminates the need for the starter box and all that.
http://www2.towerhobbies.com/cgi-bin...?&I=LXBZ17&P=7
Again I chose O.S due to its popularity and ease of tuning etc, great for a beginner in my opinion.
You would need a different type of glow heater to start this engine since you wont have the starter box battery to start it.
Something like this:
http://www2.towerhobbies.com/cgi-bin...?&I=LXJ802&P=7
You would also need a battery for this, you will find comments in the notes about that.
The pipe and header should be in your kit, both these engines will fit as most will.
Now thats the internet side of things and accounts that you can put all this together and make it work, which is not hard BUT if you have a good local hobby shop your best bet might be to grab most of your stuff there. That way you can get support and get the needed advice, given you are going to pay more for it but I feel its a reasonable price.
If you do not have a good local shop, then stick with the internet and on with the thread.
Well thats all the time I have for now, thats a bit for you to chew on.
There are lots of very good people here on this forum, Im sure we can get you going if you choose to go the internet route..