Mortgage advice

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I'm about to leave a job and will be looking for one. I've seen a fixed term contract role. I'm thinking of selling and moving house next year.

Would being on a fixed term contract affect getting a mortgage?

Alternatively if I found a permanent role but was there for less than six months would that affect getting a mortgage?

For context I'd be looking to borrow maybe 20k - 30k more.

The other option is that I live in shared ownership currently- I could staircase here and buy a bigger share then take the mortgage with me. Would that be allowed instead? Or would the fixed term contract or being in a job for less than six months still affect staircasing?

I am starting a new role in 3 months and we have made an offer on a house. Broker said there are a few that won’t lend but plenty that will (high street lenders) all they need to see is a signed contract stating start date and salary.

The 6m in new job will not be an issue for most lenders as long as there are no big gaps between jobs
The fixed term contract will make things more difficult