In terms of sizing, if you are of average proportions, I'm sure a 56 would fit you. I'm 5'9" with very short legs for someone of my height, and my 54cm Paddy Wagon (with sloping top tube) fits a bit snug, but great otherwise.

You're looking at a pretty expensive conversion if you purchase that bike. At the bare minimum you are going to need a new rear wheel, chain and (more than likely) chainring. The Miele you are looking at is using Biopace chainrings, which might cause issues with a fixed gear setup. Biopace chainrings are slightly egg-shaped to reduce strain on the knees at a certain point during the pedal rotation, and as a result of this, when tensioning your chain, it is more difficult to find a balance between tight enough to not fall off when you go over a bump and loose enough to not cause binding as the chainring rotates through it's full off-round shape. Keep in mind, however, the great Sheldon Brown rode a Biopace fixed gear, and he seemed to like it quite a bit.

If you want a cost breakdown, I would guess:

$100 for new flip/flop rear wheel
$20 for a cog + lockring
$10 for new freewheel
No idea how much new track chains cost, let's say $20?
$30 for a new chainring

If you had the conversion done at a bike shop, probably tack on an extra $60 for labour. If you did it yourself at the CBN, probably $20 in mechanics time + shop use time.

Coming to a grand total of... $200 or $230, depending on your choice of labour.

You could probably talk the owner of the Miele down to $300 without too much issue, and you could probably make some money back selling off the old components, but you're still looking at almost the cost of buying a new bike to do your conversion.

You can still snag some completed conversion deals for much less than that on craigslist, but you won't get nearly as nice a frame as that Miele.