You are deluding yourself. No doubt you'd like to see yourself as a perfectionist. The challenge you're facing, in the context of this bike, is that you don't understand what 'perfect' looks like and, despite best efforts of us on here, I don't think you're going to gain that insight any time soon.
This neglected bike has probably had a prang and the rear wheel has been replaced with one with a 9sp cassette on, despite the fact that it's 8 speed (when it was sold by
Halfords to your brother a few years ago). I suspect it has not been ridden since. I recommend you hand it back to your brother. The LBS you have booked it into on 29 May expects to replace 2 spokes, true both wheels, fit a rear gear cable and index the gears. £50 seems OK.
But the LBS doesn't know you need the cassette and (therefore) the chain replaced too. The LBS should but may not have those parts. Fitting cassette and chain is a max 10 minute job.
A cheap wheelset (front and rear) with an 8sp cassette fitted and a new chain will cost at least £140. But you're a perfectionist. I don't think you'll be content with a wheelset (ready to ride) which you can buy for less than £200.
If you want to get out and ride a bike, buy one (for £300 say), in good working order: one that's the correct size for you too. Clearly if you can envisage spending £230 on shoes and pedals then you will be prepared to buy a nice bike you can enjoy riding in the sunshine.