Note - it seems this achievement can glitch if you buy the property in person. To be safe, buy the property through the website.
This can be done relatively early on during GTAO, and hopefully this solution will save you some cash.
Firstly, DO NOT buy any garage separately for this achievement (the ones that cost 30k ish)
To unlock the achievement, you need to purchase a house, a garage and have an insured car.
You get the insured car during the tutorials. If you lose this, just reinsure another (after tagging it). The tutorial shows you how to do this.
Now, the cheapest garages are around 25k. Don't buy them, as mentioned earlier.
The cheapest house is 80k I believe. I paid 87k for my first in Vespucci beach. You'll see in the description that this house 'comes with a 2 car garage'. This garage counts towards the achievement, making buying a 25k garage a complete waste (for the purposes of The achievement in the cheapest/fastest way). Obviously if you want more personal cars, buy one.
So, for around 90k you can bag yourself this achievement.
If you don't wish to earn the money legit, for £1.99 (UK) or $2.99 (US) you can purchase 100k for GTAO. I'm unsure of prices for Europe, and AUS so if someone comments ill edit in the info.
EDIT - If you are victim of the glitch, save up enough cash to buy the cheapest apartment, 80k approx. Buy it off the Internet, and as soon as the achievement pops, power off your xbox. When you reload you will still have your money.