I'm planning a very similar job at the moment. Probably DIY as I've struggled to find interested tradespeople.
This website is very useful and authoritative:
www.pavingexpert.com/dpc01.htm
Especially read the Workarounds section on the above page in relation to your damp proof course (DPC) and the depths you need to dig to.
This video is udeful in terms of seeing the process:
Are you going to put a pipe in the bottom of the trench? I probably won't - just dig 20/30cms down and fill with pebbles to well below the DPC.
It's tricky getting into the gap between a paved area and the house wall. Especially if it is narrow - mine is 20cms max.
Will end up using narrow digging tools and lots of backache.
I wouldn't use a cutting machine near the wall of my house unless you are very, very, very sure about where all the GAS - WATER - ELECTRICITY pipes and cables are located.
Be very careful about all of these - dangerous and expensive to fix if cut.
If using tradespeople, builders and paving or groundworks people, even landscapers are often skilled at this. If you put drainage or landscaping hard into checkatrade - you will find local firms and can check their websites to see if they do drainage.