Search And Delete
Following the target is pretty simple. Consider this a training mission for later, more difficult following jobs.
Easy As Can Be
The main objective (after boosting the car) is to stay on the GPS track going back. With all these guys after you, shooting up your car and crashing into you, it's easy to miss a turn, and then you are in big trouble.
It is more important to drive carefully than quickly. If you crash, you are done. Keep an eye on the GPS for upcoming turns. Once you get near Brucie's, the bad guys will stop coming after you.
If you have difficulty with this, do a practice run. Before you jack the car the first time, look at the Pause Menu Map and note its location, then continue the mission, but if you fail, go back to that spot in the alley on your own time, set Brucie's garage as the destination, and practice the run, noting where the tricky turns are.
Out Of The Closet
It appears that no matter how you take out the target in the café, people with guns are going to be waiting for you outside, so start with full armor and be prepared to run and gun.
This is a race using Brucie's car. You start at the back. Be holding the // accelerator during the countdown so that you can take off as quickly as possible. If you jump to the front right away, which appears to be a random factor, you can win easily if you know where the turns are. If you don't jump to the front right away, you are unlikely to win.
In the latter case, pause frequently to bring up the map and mark the route of the race, then go back on your own time and drive the route to get familiar with the locations of the turns.
Once you know the route, then it's pretty much a case of repeating the race until the random factor lets you jump to the front at the start of the race.
Brucie's Side Missions and Favors
Brucie will send you emails asking you to boost vehicles for him. These side missions can make you some money and get you in good with Brucie.
Brucie will also call you to go out and have fun with him which also builds up his good will. Once you have sufficiently befriended Brucie, you can call him up and get him to send a helicopter out for you.