'that make me' or 'which make me' and when to omit 'that'

Should I use ‘that’ or ‘which’ in the following sentence?

My teaching experience and technical background are not the only factors which/that make me a suitable applicant.

Additionally, how do I know when to omit ‘that’ from a sentence? For instance, consider these sentences:

It was during those 2 years that I began comprehending the sophistication of techniques employed in the industry.

It was two years of my life that I enjoyed thoroughly.

I am confident that I can make a positive contribution to your organisation.

In which of the above should I omit the word and how do I know when to do so?

Thanks