The contracted out bit ..... if you were contracted out due to an employers pension, your NI contributions still count as a year, but at a reduced rate for each year (in the new state pension scheme). So you can have 35 years, but still not get the full new pension rate at retirement (not sure how much they deduct, but about 12-15%). Now, you can top up with extra contributions (or keep working) and each new year will replace an older discounted year (as i understand it). But that means in reality you are only adding about one sixth of a year for each year paid. May be worth it for some, maybe not. And remember your extra pension may result in more income tax ......
I was unfortunate to have been contracted out, so lost a fair bit under the new state pension rules (one year too young) - I ended up only ONE POUND better off than under the old pension system, but without the benefits like married pension rate/survivor benefits (which would have been really useful with a Thai wife)
If you do not have 35 years to start with, topping up is a good idea.