Ahh the TL-01..
For parking lot racing your fine with that car for now. For better handling, I would go for the Long Arm Suspension Kit. This hop-up it a bit expensive (half the cost of the kit) but it should handle much better then before.
I would get adjustable options (There are many)
These are used to adjust your camber, very useful.
The Carbon Shaft will lighten your car alot and improve it's acceloration.
Another must are BEARINGS. Make sure you have them. Do a search on ebay and you can get them for about $20 a set.
Since your racing in a parking lot, I would imagine that its not perfectly smooth. Those friction shocks that come with the kit are going to give you a bouncy ride. I would say get some oil shocks. These in particular:
Those will actually lower the car's ride height too.
Now for some speed. I would stay away from those Tamiya based motors. I would get a stock motor (Monster stock and P2K2 are both good) and the Trinity Comm Pen. (I'm imagining you dont have access to a comm lathe.)
Get a 23 tooth pinion as well. ( Don't forget to get Metric one's). The 23 tooth would give you more top end speed with a slight decrese in acceleration. It also lowers the life of running on the lot. Speed Tuned gears would change you overall gear ratio and change the top speeds as well.
It's going to cost you a pretty penny trying to get your TL-01 to handle at least decent. I would say learn the knowledge of RC and pick up a used or new TC3. These are excellent cars and would definatly not need to spend as much money to get it "fast".