guttering first
it is quite a small job and fixing it will prevent damp damage. there are gutter specialists but roofers also do it.
repointing is a very simple job, but tedious and fiddly, a bricklayer can do it but may give the job to his apprentice or labourer. A scaffold or tower makes it much quicker so I had mine done while the roof was being done.
try to get recommendations for local building trades from local people you know and whose opinion is likely to be valid. for some reason parish magazines are a good source of local traders who have been in business for some years and are trustworthy. members of the congregation will tell each other if they are no good.
avoid the websites that people pay to be listed on, and can remove unfavourable reviews. Even if they claim the trades are checked or rated. You have no way of knowing which reviews were written by the traders mates or his mum.
Keep an eye out for neighbours and other local people having work done. Make a note of the address and the company phone number and name on the van. Look out for signs such as turning up every day and not spinning out the job or leaving the site untidy with heaps of rubble, tools or bags of cement left in the rain. Working at height off ladders is not as impressive as a person who has a scaffold because a reputable company will have insurance and the policy will say it is not covered.
After it has been finished for a few months, walk past and see if it still looks good. If you are affable you can engage the homeowner in conversation and they may boast about what a good job it was, or moan about how terrible. Only use people who are local and have an address. Anybody can hide behind a burner phone and a fake website.
if you can find a few good local people, they will know others in different trades. Good plumbers hang around with good plasterers who know good brickies. they will not want to ruin their reputation by recommending disreputable people.
crooks and chancers also hang around together, because nobody else wants to mix with them.
When I retired to the seaside I was surprised at how difficult it was to find good people because I no longer had a position in the community and a network of contacts. I have a friend in a local voluntary group whose husband is a roofer, so he does my roof and gutters, and knows other builders and plasterers.
when you need somebody with training and a qualification, look at, for example the boiler manufacturers lists of approved installers (and check them as gas safe registered) and for electricians, I use NICEIC, there are several others.
It is true that a registration is not a guarantee of quality, but IMO it is like getting into a licenced taxi. You wouldn't choose a driver who hadn't got a driving licence.