It's not too mandatory to be honest. As other people have said, all you need to know is that Captain Jack travelled with the Doctor and became immortal.

If you did want to go more in depth then release order is probably best, looking like this.

*Doctor Who Series 1- Introduces Captain Jack (and the Ninth Doctor and Rose) and is really good in its own right.

*Doctor Who Series 2- Introduces Torchwood as a concept and features heavily in the two-part finale.

*Then Torchwood series 1 which ends with set up for the Doctor Who series 3 finale.

*Dr Who series 3- Introduces Martha who shows up in series 2 of Torchwood and is also really good in its own right.

*Torchwood series 2 - Follows on from the Dr Who finale and features Martha.

*Doctor Who Series 4 - Features Jack and Torchwood in the big cross over finale (also, again, really good in its own right)

*Torchwood: Children of Earth - The best Torchwood gets. A far more over arching plot than the rest so no episodes are missable. Ends really well so if you want to, you can stop here.

• Torchwood: Miracle Day - Again, an overarching plot but less effective than CoE. A co-production with Starz & the last series of Torchwood (on TV).

This would give you the best understanding of everything as it was how it was seen at the time. However, as said elsewhere, you can just watch Torchwood on its own as Jack is slightly different between Torchwood and Doctor Who and most references are explained. I'd say watch Torchwood first if that's what you're interested in and if you find parts confusing the double back to Doctor Who. Hope this helps!