Is it important to have a road bike shoes and pedals or it won't make a difference?
First, note that if you're new to clip/clipless systems, it takes a while to get used to it. 

A lot of non-racers prefer mountain bike clipless pedals (e.g. Shimano SPD) since you can clip in on both sides of the pedal and the shoes often allow the cleats to be recessed (so you can walk around). Mountain marketed shoes generally tend to be more comfortable as well.
An example SPD pedal is:
 

Note that some SPD pedals also double as platform pedals, so you can use regular shoes. 

Road pedals (e.g. Look/ Shimano SPD-SL) have larger support for the shoe but only allow you to clip in on one side of the pedal. An example of SPD-SL is:



However, at the end of the day, the pedal-shoe combination is completely up to you. You could use road platforms, toe clips, mountain bike clipless, road clipless, etc. - do what makes you most happy.

See this excellent question as well for comparison of pedal-shoe systems.