I just downloaded the pax.Z file for Datacom/DB, then I went to the maintenance search and there are many ptfs for CA Datacom/DB 15.1.

Do I have to download each individually?  What is included in the base?

Release : 15.1

Component : CA Datacom/DB

The pax.Z file is the base product installation package. 
To download the base product package, go to support.broadcom.com >> Product Downloads >> Search "datacom" >> Select Datacom/DB MVS >> "DVD0000000004597.pax.Z"
To see what maintenance is included in each of the base packages refer to the: Datacom Release and Lifecycle Dates, for each service pack was released by the "GA Date" column.

Note: The client should always download the latest service pack (Syymm) if one is available.

Also, you do not need to download each PTF individually. To download multiple PTFs at a time please follow steps below: 
As an example, Datacom/DB 15.1 S2101 includes all maintenance updates through December 2020 To download additional maintenance past Dec 2020 you would need to:

1. Sign in to https://support.broadcom.com/
2. Click on Mainframe Software
3. Click on Product Downloads
4. In Search Your Product type datacom
5. Click on DATACOM
6. Click on Solution Downloads tab
7. CA Datacom/DB MVS and click on 15.1.
8. This will show all current PTFs
9. Change SHOW PER PAGE to 100
10. Filter the results by entering a date in the SINCE: field. Enter 01/01/2021
11. Currently, there are 83 PTFs 
12. Click ADD ALL TO CART
13. Click on Cart in the menu line
14. Scroll to the bottom and click the blue button under Complete PTF package, it will turn grey
15. Click on Checkout
16. In the Cart History download the cart zip file
17. FTP the CART .zip file to z/OS.
18. In z/OS run CAUNZIP to unzip the file. It will create an SMPNTS file
19. Use the JCL that is created in the ZIPRPT DD of the CAUNZIP job output to RECEIVE FROMNTS the SYSMODs.
20. Download the latest ERROR HOLDDATA
21. Download CA RS and HIPER ++ASSIGN Statements
22. Receive HOLDDATA and PTFs
23. Apply all the maintenance using SAMPJCL member DCM80APM

Similarly, but for Datacom/AD, check Article 209443: "CA Datacom/AD 15.1 downloading all PTFs after base installation"