Does "start off" give different impression from just "start"?
You're correct! "Start off" and "start" do give slightly different nuances. "Start off" is usually used when we talking about a series of steps. Think of it as a sequence, this is step number one and there will be more steps to come. While "started" can be used for a series of sequences, it is generally used when there's only one action that will be ongoing. Because of the slight difference, there are some cases where "start" and "start off" would not be interchangeable. Ex: Let's start baking the cookies. Ex: Let's start off baking the cookies, then we can do the cake.