Yes, the spelling DVCITIS was absolutely valid in the Roman Republic and early Empire. The introduction of the letter U allowed people to mark the difference between the sound used as a consonant (sounding like our letter w) and the sound used as a vowel (sounding like our oo). I don't know when folks started using U, though.
Interestingly, there are different approaches to spelling Latin today, too. I prefer to alternate between v/u and j/i for consonantal/vocalic sounds. Church Latinists tend to do this as well. Most other folks seem to be to alternate v/u for consonantal/vocalic V but to use i for consonantal and vocalic I. I've encountered a number of texts printed in the last several years, however, that use only U and I for both consonantal and vocalic sounds; I'll admit to finding this a little annoying to read, but it could be that I'm used to alternating V/U.
In the time of Cicero, Cæsar, and their compatriots, yes, the C would have been pronounced like K. The change to a CH sound occurred some time between 300 and 700 CE; you can read more about it and the other phonological changes from classical to medieval Latin here.
The addition of the macron to the U in later years isn't really a spelling change; it's more a visual aide to let readers less familiar with the vocabulary know what vowels are long. So in classical Rome, you might for example find misspelled graffiti that read DVVCITIS, doubling the length of the vowel. No one who actually spoke Latin as a native tongue would require macrons.
The Romans did on occasion mark long vowels, but they did it differently, with what we think of today as the French accent aigu; you can read this meta post for a more detailed discussion. However, they usually did this only to mark vowels that, if left unmarked, might cause the words to mean different things (for example, the word anus means both "anus" and "old woman," so if there was any risk of confusion you might want to avoid it by marking the vowel). However, the use of apices isn't widespread these days, and if this is meant for a general audience I'd advise against it.
So I'd say you should go with either DVCITIS or DUCITIS.