With regard to finding a good garage, have a google about and look at reviews. Honest John website has a good garages guide that may list in your area.
So, how much should it cost? Type you reg no in to the likes of autodoc.co.uk or eurocarparts and it will give you parts prices.
I've replaced the rear discs and pads on my Jazz. Purchased Pagid brand parts from CarPartsInMotion via ebay who I use often, and paid c £70.
If you've a rear brake binding and it cant be freed off, which is unlikely, then a new caliper will be requred. Brake fitting kits are c £10.
Is £1300 dear? Too right it is. Discs and pads fitted should be c £220, at least that is what Protyre quoted for front brakes on my car last year. Fitting kit, well they shouldnt charge to fit as they have to come off anyway. Replacement caliper? Certainly an hours labour max.
Just my opinion, and I HTH.
The manual if you want to see how things work is here
https://hondafitjazz.com/manual3/index.htmlReplaclement is not super complex. Threads on here (search facility) will show how it's done, or you've Youtube to search.