First and foremost, if your using washing up liquid (i.e. fairy liquid) on your paintwork - STOP! fairy liquid contains micro abrasives to help its degreasing action and so repeated use can inflict more swirls (micro scratches) onto your paintwork...
Now. polishing. I assume you will be polishing by hand? if so, one of the best products out there for hand application is Autoglym Super Resin Polish (you can get it from halfords etc). this is an All-In-One type product, which has light cutting ability and so will remove a small amount of swirls, i also has a lot of fillers in it, so it will fill a LOT of swirls on your paintwork (this is not permanent and will wash off eventually - after 4 or 5 washes approx.), it also has a mild sealant property so will sheet water off if and provide a basic level of UV and dirt resistance. This is ok and will make the bike look good for a while, but you will need to re-do this every 4-6 months to keep it looking good. using "proper" polishes can remedy the problem more permanently.
If you want to properly bring back the shine to your paintwork you should ideally be looking into something more intensive which properly cuts paintwork and will restore the shine to the paintwork in a more permanent fashion. The Menzerna range of polishes is good for this, or if you want to go old school there is the likes of Farecla G3 and G10. This is of course a much more skilled process, and there is a risk of striking through paintwork with this process (it is also likely you will use a polishing machine for this instead of simply by hand).
For general cleaning/degreasing, a dedicated wash product for vehicles is suitable (this can be something as basic as zip wash from halfords, which is only a few quid, or if you have access to Costco, you can get 25L of turtle wax wash and wax for about £20

). For degreasing I can recommend something like Bilt Hamber Surfex HD. this is a fairly cheap degreaser which is very effective. alternatively, if you want to keep thing simple, and dont want to go hunting for products: Tesco sell a cleaning product called "Daisy", which is an all purpose cleaner. this can be used for most general purpose cleanign and degreasing, and is concentrated, so you can alter the dilution ratios to suit the application. this is also only £1 for a 1 litre bottle (which is dilutable) so is pretty cost effective.
stainless steel can be polished with either Britemax twins metal polish, or autosol, and this should remove some slight scratches and bring up the shine (you can see some examples in the review for britemax twins here:
http://www.detailingworld.co.uk/forum/sh...p?t=152466 ) Again, if you want to do it "on the cheap", tesco sell a product called "bar keepers friend" which essentially does the same thing
If I were you, and was looking for a simple, high impact, low fuss (and low cost) methodology to restore the paintwork and give some good sheeting abilities, my purchase list would look like this:
Tesco Daisy (or Autosmart G101 which is essentially the same thing)
Autoglym Super Resin Polish
Collinite 476s wax
a coat of SRP and a coat of 476s on top should see you with around 6 months of water sheeting abilities and the bike should look good through this meaning you only need to clean with a very weak daisy/g101 solution in between, and use a stronger mix on the wheels/engine/unprotected parts.
rambling again....better stop now :lol