I agree with PrueM that the camera may not make a huge difference, but things such as weather conditions, time of day & condition of the gravestone will.
I too, like a viewfinder. I have two cameras, a Fujifilm s5000 bridge camera and a Canon EOS 350D DSLR. The Canon has an optical viewfinder, the Fuji has an electronic viewfinder, so the image you see is a lot sharper in the Canon than the Fuji. "Modern" electronic viewfinders are a lot sharper than my older one though.
Both of these cameras are quite old now and can be picked up quite cheaply second hand but if you want to go more modern, then new ones can be a bargain - Amazon currently have the Canon EOS 1100D at £361
I took the picture I have attached at Midday in October with the Canon, not because the grave is relevant to my research, but because I liked it.
I think it shows some of the things you will need to consider - the light was good so some of the inscription is easy to read, but there are other conditions affecting the result - the grave is overgrown so the ivy and grass prevent a complete reading. I take a notebook along to a cemetery and transcribe what I've seen, as well as taking pictures.
Good luck with your choice & I'd be interested to hear what you decide on.