What type of wheel fits a 700x38 tire
A tire that fits an internal rim width of between 17mm and 23mm wide. 

Searching for bicycle tire width rim guide will get you more information. So anything from 700 by 17mm internal width, to 700 by 23mm internal width will suit you.

If you think you likely use skinner tires in the future, stick to the smaller end of the range. If you think you'll go wide, stick wider.