Padorko->Killanov R.
Nothing fancy here. Blow up the three rocks along the way. They contain 50 gold, 400 gold, and a Gem. Gems can be traded in much later in the game for special equipment. When you get to the ruins, go to the back to get a package from the old man.
Killanov R.->Padorko
There are some stronger enemies this time. The first rock now contains 400 gold, the second a piece of Junk. Run over it to carry it behind you on your hook. About 3/4 of the way back, you will run into a more dangerous enemy. Shoot it as it runs in circle around you. Eventually it will die and you will get the CardOD12. Finally, the last rock contains a (now useless) HPRest50.
Back in Padorko, collect your money from Takah. Then use your CardOD12. Now you know the Spin 60 Overdrive. Select Overdrive in the menu and assign it to the side slot. By pressing B and left or right, you can spin your car quickly. Next, your mom will turn her house into a Garage for you.
At this point you have some freedom on where to go. First, have Takah inspect the junk you picked up. It's a NapTorch! Go back to your Garage and put it on your car using the Convert menu. Now, you can take jobs from Takah, drive to other cities, or bring your mom materials to build her Garage with. Let's go to Samoge first.
Padorko->Samoge
Stay to the left, and follow the route symbol. About halfway through is a tree with the CardOD4. This is the very useful Jump Overdrive, which will let you access places that you couldn't before. Nothing else is of note here. Try to pick up some cargo that your mom can use to build her Garage.