There's 2 things to consider when attempting what you are considering to do:
Make it road legal: that means 3 things.
a) First, it must conform to the minimum equipment list of your jurisdiction which is likely to include (but not limited to): honk, headlights, tail lights, brake lights, turn signals and wheels.
b) Second, you must get it insured, meaning your contraption needs a "manufacturer" and serial number.
c) Third, you must get a licence plate on it, for which you also need a "manufacturer" and serial number. You will likely need to pass either a "salvage" or "out of state" inspection, and most jurisdictions have emission tests as well. Those can get strict to the point where absolutely no modifications can be made to the vehicle from when it was new.
2.Is it a good idea: A car isn't like a couch or a dishwasher and driving isn't like a video game. It is a machine moving at high speed and people die from this every single day. In the US alone, 35,000 people died in car crashes in 2015. So, if your home-made contraption suffers a catastrophic failure while at speed, like the steering column snapping in 2 or an entire wheel sheering off, you will not only likely kill or severely injure yourself, you will likely take others out with you.
I believe, like you, that most new cars aren't worth the asking price, so here's what I do, and invite you to do as well:
- Go to your local car auction
- Find something you like for under $1000
- Bring a mechanic friend over to look the car over
- Budget about $1000-2000 for immediate repairs
- Enjoy your $2000-3000 car for the next 10 years.
I have owned 4 vehicles so far in my life:
- all have been bought for $3000 or less (including immediate repairs)
- all 4 are still running and in my possession
- one I've had for 10 years already (it was already 14 years old when I bought it, it had 169,000 km on the clock and just went over 309,000 km recently, still going strong)