Mulberries: you need to get the Black Mulberry (Morus nigra) for fruit, not the white mulberry (Morus alba) which is the one used for silkworms.
They're self fertile so no need to get male and female.
30ft is more typical - my 25 year old tree is probably about 20ft, and even elderly ones I've seen have been nowhere near 80ft. But their spread is quite large. No trouble with shallow roots or suckers. The RHS reckons they can be container grown for 10-15 years which would restrict growth (although half of that period would be non-fruiting) or they can be espaliered against a wall.
Clay soil is fine - mine is in clay which gets quite soggy in winter (even though the RHS says they need soil which is "moisture retentive but well drained")
The interesting article that Bob posted said that mulberries fruit in about 8 ears from a cutting. Bearing in mind that the tree that you buy will already be at least two years old, that would mean nearer 6 years for fruiting which has been my experience. I've grown them in two gardens, and both times I was surprised how quickly I got fruit (compared with the 10 years I was expecting) - just one or two the first year or fruiting, a few more the next, then abundant from the third. Once they get into fruiting they are very prolific - I already have a freezer drawer full, we've been eating the fresh ones with abandon, and we're only about half way through the cropping.
What I have found is 1) the blackbirds like them - though it doesn't really matter because there's more than enough for both of us 2) there is a total disconnect between the "fruit ripening" and "fruit dropping" mechanisms. Early in the season a lot of half ripe fruit is dropped, but there is also fully ripe fruit which hangs on until it rots. 3) picking is difficult - you dislodge too many half ripe fruit no matter how careful you are - hence the recommendation to harvest by placing a sheet underneath and letting them fall.
In terms of growth, they are the last tree to come into leaf, to the extent that you think you have lost it. They then hold on to their leaves quite late. The leaves turn an almost luminous yellow, so the tree looks like a yellow globe lit from within, then suddenly they drop the whole lot in one go.