Any linkage between contribution and membership records?
The only link between CiviContribute and CiviMember is the payment record associated with a membership. This is stored in civicrm_membership_payment table with an indirect FK to a civicrm_contribution record (since they could be potentially other forms of payment beyond CiviContribute).
You can configure online contribution pages to include a membership signup/renewal block. When user signs up/renews on these pages we automatically create:
If you are entering a Membership manually from a contact record page, I think you need to:
You could, I believe, integrate steps 2 and 3 by creating a Profile of type Contribution and including the "Add to group" there.