I used to be a big fan of buying Space Marines cheap on eBay, stripping their often terrible paint jobs, and repainting them as part of my growing army. In fact, a good majority of my models were acquired and completed this way. For example, these pictures show before and after for some of my bikers:
Simple Green and Easy Off Oven Cleaner were my tools of the trade, with acetone joining in later. The sink in the guest bathroom/laundry room was often licorice scented (from Simple Green) and paint-spattered. These days, however, I'm a total model snob. I have amassed enough parts and kits that I've not built a totally refurbished model in quite a while.
Today I was brainstorming some fun ideas for the hobby, and wondered how interesting it would be to see a full army go from junk to jewel in a photo timeline. The loose plan would be to buy an army secondhand, with a fixed layout. Take a single combined army photo, as well as individual unit photos as a baseline. Then, using a single new box set, slowly rotate the old models into and out of the paint stripping bath. You'd build one brand new model from your box set, and pull one old model from the first unit. Strip the old model while painting your "seed" model. When the seed model is done, put it into the unit and take a picture. Begin painting the stripped model while stripping a second. It's a little cycle that would allow you to document the whole process.
The rest of the box set is there to use for repairs, spares, and embellishments. For example, some models simply cannot be saved from their paint jobs. I found a whole batch of Marines I'd bought secondhand had scarring and bubbling under a super thick coat of glossy spray paint. I managed to save some, but several had had complete sections of detail burned away. I salvaged the non-burned parts, but had to replace bits to get full models.
It might also be interesting to document your costs. Get a baseline cost of the army when you buy it, plus the cost of your "seed" box, a gallon of Simple Green, and a can of oven cleaner. Keep a running tally each time you buy parts, paint, and supplies. When the project is done, it would be neat to compare the retail cost of that army to what you've spent.
I think a Warhammer Fantasy army might be easiest to document. The block layout of units facilitates nice photos and a "start to finish" progression. There are also a lot of very simple WHFB models, like the single-piece Dwarfs from the old Skull Pass box, Orcs from the Empire/Orc starter, etc. Alternatively, a 40K Ork army might work well here, as it is both an army that can be acquired cheaply, as well as an army that typically has some scary beginner paint jobs and the ability to facilitate conversions and kitbashes in order to salvage as much of the old models as possible.
Of course, I definitely don't have time for such a project any more. With a new excitement for my Marines' focus of fast attack, the glacial pace of my Nids, and life in general, I don't think an Ugly Army project would progress at anything but a complete snail's pace, making it hard for readers to follow.
Maybe in the far off future...