I am transferring a database to a new SQL Server and was wondering, will it lose it's execution plans and statistics that its collected over the years for the benefit of performance and have to start over?
Execution plans: OBVIOUSLY. As does restarting the server - these are kept in memory and generated on demand.
Which also means you never collected them over the years. Unless you have a never patched system which would be a much bigger problem.
Statistics: no, those are actually objects in the database, so they transfer.
Here you also did NOT collect them over the years as new ones overwrite old ones.