I think you have answered your own question there ,, looks like you really want the lathe .
From my experience , the two are completely different tools that compliment each other ,,
I have always found the mill to be the more versitile machine ,, but that will always depend on what you are making .
Oh , yes ,, bigger is definately better .. grin ..
When choosing the lathe ,, look for the largest hole up the center of the headstock that you can afford.
My preference in a mill is the old but sturdy Bridgeport , a very versitile machine . Add the 3 axis digital readout ....... hmmm ..... and you've really blown the budget , LOL .