Washing a car is a personal thing - In terms of how people do it and really what the car is used for and how much time people have.
I'm know I'm probably over the top with my cars but it's just how I am and what I have learnt - my exterior winter detox can take up 4 days. - My HDi when I got it took 2 weeks to clean down
In this scenario, I'd probably say go to the jetwash and clean off as much dirt as you can, getting the washer under the arches and around the lower sills etc. - I wouldn't brush the car off etc, just literally use it as a pressure washer.
Then go home and get your two buckets - one for washing and one for rinsing, then clean the car down as you normally do. - By pressure washing the dirt off first you are minimizing the impact of causing extra swirls by dragging dirt across the paint with a sponge.
Use a mild car shampoo and rinse the car down each time rinsing out in the rinse bucket. Here I would use different brushes to get around the badges and tightwork, even armed with an All Purpose Cleaner spray on the tightwork and around window edges then rinsed down with the shampoo.
Get as clean as you can then after rinsing I'd recommend buying a large drying microfibre cloth to dry as these are more effective than a chamois ( no streaks etc ) and will be better for your paint.
Once dried, I'd use a filling product to minimize the swirls - i.e Autoglym super Resin Polish, then go over with a decent wax to protect the paintwork and lock the glaze in.
Use wax all the time as it acts as a sacrifical layer of protection for you paintwork and makes the cleaning process that much easier.
If you wanted to take it further, then pick up a pack of microfiber cloths and clean down the door jambs/shuts etc. - this can be done easily again using an APC spray and a few brushes - and due to you limited access i.e up and down stairs with buckets, maybe pick up one of those 5ltr pressure sprayers ( like for use in gardens etc ) wilko's QD etc do these for about £7 - Use the pump spray to clean down the door shuts then wipe around with a cloth to clean.
Again the above is what I'd recommend to get a decent clean done with limited access, your right, Black will pick up many scratches easy if not looked after but at the same time it's the most rewarding colour when clean.
The danger with hand car washes at £5 a time is that they will induce swirls pretty quickly and effectively for your £5. - The TFR they use is very high strength ( causes paint fade and damaged to lacquer alloys and center caps ) - the big wash tub they use as well when dragging mitts over your paint is full of dirt so basically they are dragging it over you paint and your paying them to do this.- You only have to look at the state of the paintwork on your local taxi's around town... they will pretty much demolish the paintwork.
My advice, never take your car to one of these local hand wash jobbies - all when and good if it's a tractor used around the farm but your personal use car > no way.
or get a Beige car!
then Paint-Cleaner, Polish and Carnuba Wax.......only took 3 hours 