You should ______ swimming.

From MacMillan Dictionary:
Take up:
to start doing something regularly as a habit, job, or interest
Examples:
I took up smoking when I was at school.
Chris has taken up jogging.

Start up:
Meaning: to bring a business, organization, or project into existence
Examples:
The Agency helps over 1,000 firms start up each year.
She left the company last year to start up her own business.

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Take up (PHRASAL VERB):
take something ↔ up
to become interested in a new activity and to spend time doing it.
Example: Roger took painting up for a while, but soon lost interest.
She took up tennis at the age of 11.
You should take up swimming.
Source: Oxford and Longman Dictionary of Contemporary English.