Typically conversation scope is used in multiple HTTP request/response cycles like a wizard or multi-page form, etc.
Do you have multiple HTTP request/response cycles in this use case (i.e. multiple form submissions)? If yes, then you can model this using a JavaBean or SFSB with conversation scope as the backing bean for your JSF view. But it sounds like your use case spans one or two pages maximum. Request scope may be suitable here. After step 1, is the user still on the first page or a different page?
@Begin promotes a temporary conversation to long-running (LRC). The @End demotes to temporary (for eventual destruction).
Read the ref doc or SiA book for more details. See the hotel booking example as well.