Your character at the start of the game is too weak to actually fight, so avoid combat altogether (random combat encounters, gang-rape events, police searches), use hole-in-the-wall shortcuts as often as possible, eat at restaurants when you have to fill up and have money to do so, and so on...
However, you have to deal with the compulsory 2 enemies at the end of each delivery run, so make full use of weapons instead of normal attacks. One way of accumulating weapons is to get into combat encounters (random ones for now, provided that the enemy do carry weapons) and bribe/seduce them so that you can grab their weapon and use it on them.
That should be enough to clear the first route. Just repeat the 1st route once you get a good understanding of the gameplay loop.