The trouble with fixed rate mortgages is the bank needs to factor in the extra risk in interest rates rising so you probably will be paying more, especially if you choose fixed rate over the long term. Apparently though they profit as much from fixed rates as variable rates, and they charge fair penalties for customers switching from fixed to variable rate.
If you can comfortable afford to pay a significant rise in interest rates variable will seem like the fairer deal. The interest rate will hopefully be more correlated with the ecb rate and you have the flexibility to increase or skip payments without penalties. In the shorter term (<2 years) your payments will likely be lower too.
But especially for people just starting out and have their finances worked out to the penny, fixed rate gives you added security and protects you against hikes in the interest rate. And when interest rates are low this is reflected in a lower fixed rate.
I'm not too up to date on what all the banks are charging but it looks like you're getting a good deal with the 3.99% fixed for 3 years.