Hi Tracey and welcome to the forum, you have come to the right place for advice. Most people will tell you to rent first, A: to see if you really like your chosen area, and B: to give yourselves more time to get to know your way around before committing to anything as major as property purchase.
Banks, well yes spread your money around the Government guarantee here only cover up to 100K Lira per person per bank account. Which banks, people have their preferences, we've banked with TEB for around 6 years and had no complaints, we also have accounts with Garanti and ING.
Have a look via the search facility on here and you will find lots of advice. Good luck with your planned move.