TDE will impact compression of backups, because backup compression is applied on top of encrypted data. However, TDE has no effect on table and index compression, because TDE is applied on top of pages and rows. So, TDE should have no impact on the online storage requirements of your database.
Also, I've never seen TDE add more than a 2% impact to read or write throughput. However, it probably depends on the specific data access patterns of your application. Compression, in general, requires more computation for writes than it does for reads, and most of the databases I work with on a daily basis tend to be large, write-once, read-many, and are typically bulk loaded rather than high transaction volume. When it comes to performance impact of compression, your mileage will vary.
"Do not seek to follow in the footsteps of the wise. Instead, seek what they sought." - Matsuo Basho