Whether you prefer stools and chairs with or without arms is purely a question of personal taste. The arms can potentially provide extra comfort, but the lack of arms provides greater freedom of movement. Some people actually like to rest their elbows while eating or drinking, while others may find the arms actually get in their way. If you have decided on stools with arms, then the other factor to consider is style.
I like all three of these… now if I only had a bar:
Barstools with arms pictured:
Left: AmeriHome BS1061BSET Adjustable Height Bar Stool Set, 2-Piece
Middle: ACME 07031 Swivel Barstool W/Armrest
Right: Pastel Furniture GL-217-30-FB-865 Glenwood Swivel Barstool with Arms, 30-Inch, Feher Black and Black Leather
There are very modern looking barstools available, as well as more traditional styles. Usually, matching the look of the stool to the look of the bar or counter it will be next to is a good idea. Modern stools for contemporary counters, and more traditional ones for other styles of decor. Of course, if you are more experienced decor-wise, you could go for a contrast of styles.
Not all stools are the same height, and so you should make sure the one you pick will be right for the counter you will be using it with. This is especially important when the stools have arms. What you don’t want happening is having the stool’s arms hitting the counter, stopping you from getting close enough to be comfortable.