If you like someone (and this person feels the same about you), is it best to start as friends and really get to know each other or jump right into dating?

Just start dating, friendship comes along with that.

Don't jump into a relationship right away they rarely last
Go out and get to know each other.
Too many jump right into a relationship thinking the package is what it looks like only to find out they are not compatible, the other is a grouch, the other doesn't appreciate you, they do not spend time with you, take you for granted, etc...

I totally see what nohelp4u is saying but there was a guy that I went out with for quite a while and we wondered why we were just friends so long and never dated.

It is best to start with no expectations and once you are comfortable take it further
Of course the opposite can happen and you remain friends longer than necessary but at least you are together and have the opportunity to say hey why hasn't our relationship gotten further than it is.

Do what's comfortable, and have fun at it and see if the interest is mutual, and don't assume its as intense as yours is, but its fun finding out. Go slow, and get to know one another.