There are a variety of companies that make cycling computers. Vetta, CatEye, and Sigma Sport all immediately come to mind. All those companies make a range of products. More expensive models have more features, not better accuracy. Even the basic models though will have some standard features such as average speed, current speed, distance ridden, time ridden, etc.

All computers work fine with all bikes.

I'd look through the above companies web sites and determine which one you think looks good, seems simple to operate for you, and go from there.