Thanks
@RecordAceFromNew , what do you think would be the best way to got about it. Do you think a trip to the LBS, with the bike, would be better for advice?
I don't know what the answer to your question is, because the answer is dependent on whether you are happy to learn, buy some tools* and experience diy, or would you rather pay someone else to do the job for you. All I suggested above was which components I believe are decent and good value for money and would work for your purpose. It is always interesting to ask your lbs' and see what they suggest - it may tell you something about whether they know their onions and whether they have your or their own interests at heart... The other thing is only you can decide how low you want your new low gear, which is dependent on what hills you want to tackle, how fit you are, and whether you would mind walking up the occasion hill. Regarding the decision of compact chainset or alpine cluster, apart from the former doesn't go as low as the latter, your preference may also be driven by whether you would mind a rougher front shift (because front shifts are agricultural at the best of time and a compact is not going to improve it), and whether bigger steps between rear gears will bother you (it doesn't bother me - I have a 1x8 that I am perfectly happy with but ymmv). What is clear is the lowest gear of your bike is unusually high for the average rider/terrain.
* If you are comfortable with diy practically all you need to know for repair and maintenance is in
this guide, and for a rough idea of costs practically all the tools you likely need for most bike maintenance/repair jobs are in
this starter kit plus
this for freewheel removal and
this for cable cutting.