Are There Any Rules About What Is Suitable As A Communion Wine?

Not really, at least no absolute rules. Probably the most important guideline is that the wine should be natural – that is to say, it should not be fortified but more like a table wine.
It doesn't matter whether the wine is red or white but it often tends to be on the sweetish side because it is more palatable after one has been fasting or for early-morning communion. For Jewish people observing the Passover feast, sweet wine is prescribed because there has been a fast previously.
These guidelines are the ones approved by the Church of England and the Catholic Church.
Some distributors offer stocks of communion wine that has been approved for the purpose by the appropriate religious authorities.
On occasion, where the prescribed elements are missing, fortified wine and even spirit has been used. Take for example Lord Strathlan, dying on the battlefield at Culloden in 1745. Whisky and an oatcake were substituted for wine and wafer − they not being available.
Any branch of the church which eschews fermented drinks usually substitutes plain grape juice.