Should I start my PR application on the ICA website and then ask my HR for the required letter? Or, should I get the required letter from my HR and then apply on the ICA website?

There are two different documents you need from your company for your PR application. One is the form Annex A, and the other is an employer's letter. Form Annex A is downloaded from the ICA's website with your PR application form, whereas the employer's letter can be issued from your company. It is totally up to you whether you want to receive the employer's letter before starting the application or after you start the application, considering Annex A can only be filled after you start the application. Just remember that the company has no right to stop you from applying.

The best approach is to prepare all documents and ask for letters from your company a week prior to starting the process.