Hi Grampa,
If we were to pick out one product for each of the stages you've picked out, these would be our suggestions:
Wash - Lusso Auto Bathe. This shampoo is a pH neutral shampoo that is incredibly lubricious, smells delicious and has an excellent dilution ratio so is great value for money. The Dodo shampoo recommended by Trix is also an excellent shampoo, but the Auto Bathe has the edge for me as I think it leaves a glossier finish, makes slightly more bubbles and most importantly to me, smells of coconuts, which I love!
http://www.autoperfection.com/shop/Luss ... 237ml.html" onclick="window.open(this.href);return false;
Polish - Dodo Juice Need for Speed. We have to agree with Trix on this one - if you're looking for ease of use then this product has got to be your number one choice as not only does it polish the paint work, but it also leaves behind a protective layer that means you don't have to wax over the top of it if you don't want to (you can of course still apply a wax or sealant on top if you want to, but with this product you don't have to if you're pushed for time or simply don't want to!)
http://www.autoperfection.com/shop/Dodo ... 500ml.html" onclick="window.open(this.href);return false;
(This does also come in a 250ml bottle, however, I've linked to the 500ml bottle as you will more than likely need the larger bottle due to your dedicated cleaning regime)
Tyre Dressing - For this one I am going to recommend two products, simply because I'm not sure if I've understood your requirements correctly! I read your question as if you were asking for a tyre dressing for the tyres, however, Trix has answered as if you're asking for a product to treat the wheels themselves, so I thought I'd just make my suggestions for both to be on the safe side!
For the tyres themselves we would recommend our own Tyre and Trim dressing, which can simply be sprayed onto the tyres and left to dry so couldn't be easier to use (you just have to be careful if you're doing this on a windy day, as sometimes the wind can pick up the spray and carry it down the side of your freshly cleaned car... in this instance, you might be better off spraying the product onto an applicator and applying it to the tyres by applicator).
If it's the alloys themselves you're looking at, I would have to go for Poorboys Wheel Sealant, as in my opinion it's easier to buff off than any of the others I've tried. It's not the most expensive top-of-the-range product, but I think that the Poorboys Wheel Sealant is a bit of an underdog, as it's sometimes overlooked because it doesn't cost as much as some of the alternatives. In terms of value for money, ease of use and the results that are achieved, I think this one would be a hard one to beat.
http://www.autoperfection.com/shop/Auto ... 250ml.html" onclick="window.open(this.href);return false;
http://www.autoperfection.com/shop/Poor ... t-8oz.html" onclick="window.open(this.href);return false;
And finally with regards to the mitt and whether it's worth it, my answer would have you a resounding yes. The problem with a sponge is that it has a fairly solid surface, which allows any dust or dirt particles to sit on the surface, which then in turn get scraped across the surface of the paint and can cause swirl marks and scratches. With a wash mitt, whether it's microfibre or lambs wool, the fibres are much longer than they are on a sponge, which means that dust and dirt particles get trapped deep within the fibres and are held well away from the surface of the paint. One of the ways to avoid this is as Trix has said, to use the two bucket method. If you're a real stickler for easy routines and regimes, then you may want to stick with just one bucket and this is also perfectly fine - the one thing we do always recommend, whether you're using one bucket or two, is to have a grit guard in the bottom. Each time you dunk your mitt into the bucket make sure you scrape it across the grit guard at the bottom of the bucket and this will work loose the trapped dust and dirt particles, which then sink to the bottom of the bucket and are held out of reach by the grit guard.
If, like me, you prefer the feel of a traditional sponge shape, rather than a mitt, I would recommend using a microfibre wash pad.
http://www.autoperfection.com/shop/Auto ... d-Kit.html" onclick="window.open(this.href);return false;
(We do also sell a double bucket kit if you did want to go for the double bucket method)
http://www.autoperfection.com/shop/Auto ... h-Pad.html" onclick="window.open(this.href);return false;
Hope this helps!
All the best
Taryn