Iran is very different from what you hear on the news. Of course, it has a strict regime enforced after the 1979 Islamic revolution, but nowadays it seems that the regime slowly becomes more liberal, travellers are welcome (although there are still very few foreigners), people are incredibly hospitable and the ancient Persian culture is what makes them proud.
Flights are inexpensive from Europe - we arrived through Kiyv-Borispyl. Nowadays, you get a visa on arrival in the airport. It took us 4 hours, but better than sending your passport somewhere before the trip. Make sure your travel insurance lists Iran specifically, otherwise you will have to buy a new one and stand in another long queue.
Iran proves once more that people don't like something that is enforced on them - Iranians are much less religious than many other more liberal muslim countries. On the contrary, Zoroastrianism, the original Persian religion that inspired Judaism, Christianity and Islam, is very much respected.
Travelling around the country is quite cheap and convenient with buses. We did that, but also rented a car in Esfahan in order to better enjoy the desert and countryside. We had a good experience with Europcar, but bring lots of cash - even the deposit cannot be paid by credit card. Iran is still financially isolated. To my surprise, I got the traffic fine deposit back to my account a few months later from Kuwait.
As a practical warning, after visiting Iran you will also loose the ability to use ESTA to travel to the USA. You can still get a full US visa, which I already have without any problems. Apart from that, architecture, cultural legacy and landscapes are really worth the trip.
As a side note - try to avoid Nowruz, Iranian New Year held in the end of March, as Iranians have holidays for two weeks following it. All the popular sights get very crowded, some interesting ones are closed, traffic gets more dangerous and you have to make thousands of selfies with locals who don't see foreigners too often.
As usual, the rest of the story is in the comments below.