New bar tape is one of the simpler upgrades you can make to a road bike. Fresh tape can change the look of your bike, and dramatically improve the comfort. From a safety perspective, your hands are more likely to stay where they should be if you are using quality tape in good condition.
Grips are considered a less consumable item than tape, often slide on grips will last the life of the handlebars if not the bike. In the past we have been lucky enough to come across vintage grips from the 1950's that were in great condition.
Various materials are available, they all have different merits. Leather and synthetic materials are generally hard wearing. Cork is lovely and comfortable, cloth grips well and looks great on retro bikes. When it comes to slide on grips the synthetic materials tend to last better, particularly in areas with harsher weather.