Pro Res looks perfectly fine on big screen as long as you have a competent projectionist. It also would need something to play off e.g a Laptop - and can be a little bit fiddly to set up. I did a screening off pro-res using my laptop at my local odeon and the "projectionist" looked on confused as I had to pull out the non sync CD player cables to get audio from the laptop into the cinema sound processor. Easy enough - but commercial cinemas may not have a skilled projectionist any more.
Your average multiplex probably couldn't cope with prores, but more and more cinemas have the resources to screen alternative content. If they are happy to screen a pro-res then that would be easiest option, I've screened my work off prores in several cinemas and it looks perfectly fine. But as Tyler states its probably less robust, if you running off a laptop that could crash or overheat Vs a dedicated cinema server.
If they ask whats a ProRes? Then you have your answer, start looking at DCP
DCP is probably safer and as stated above it shouldn't cost you anything to make - the free version of resolve with do it, the latest version of adobe premier will do it and you can also get http://dcpomatic.com/ which is a free as well.
The only issue with DCP's is some cinema servers are picky about the format e.g it has to 24fps on a specific disk format - EXT 2/EXT 3. You might get away with other frame rates (e.g 25) and disk formats (e.g NFTS) but its dependant on the cinemas server.
If this is the premier its probably a good idea to have a back up so if your using a laptop to screen a prores, I'd try and have two laptops and two copies...
A good cinema should allow you to do a technical rehearsal, even if your screening off DCP its worth checking it. That would give you a chance to ensure gamma, audio levels, audio sync etc... are ok.