should I buy a fancy new bike which will break down and cost me lot of money in repairs
On the contrary, if you get a new bike, like a new car, you should not expect it to break or need repairs for quite a while. And it will likely have a warranty for the first year or so.

If you get the right bike, you'll be way more comfortable, the bike will be lighter, and it will be much easier for you to start riding faster. You might even want to ride more than 4 days a month.

Just remember, fit, fit, fit. Get a bike that fits right. Check out some of the threads here on choosing a new bike, there's lots of good advice.

We have a 25-year-old Fuji in the garage. It's really cool, but very heavy! My bf converted it into a single speed for fun.