I would go black counterand something like this for backspash.

I would probably stay with a more neutral counter top like the ones attached. They will go well with the bright walls now and if you decide to go with a different color later, you won't have to worry about the counter tops matching. Or, for a more organic look, you could do butcher block tops.
https://www.houzz.com/photos/3458-travertine-silver-180fx®-with-ogee-idealedge™-cincinnati-phvw-vp~553798

I was thinking about white subway tile or just painting my current square tiles white... I agree with both of you that black or neutral would look best...but what do you guys think of 3420 Dolce Vita or Dolce Macchiato 180 fx countertop? Do you think they would match?The green colour I plan to use is like granny smith, that type of bright green.

Artisan Kitchens, I like a lot of countertops, for example, the first two pics Madden showed, I like both those but I also like the black or brown countertops...I'm looking for neutral countertop that could go with various paint colours but I REALLY want a bright green kitchen, and I don't want to end up with a countertop that doesn't look nice with the colour of green I want.

It looks like either one of these could work especially with the white cabinets and the white subway back splash. What does your floor look like?
https://www.houzz.com/photos/3420-dolce-vita-180fx®-by-formica-group-with-bullnose-idealedge™-kitchen-cincinnati-phvw-vp~553222

Black, Dark Grey, or possibly a Bianco Carrara or Calacatta Gold marble may look good.

the attached pic is my current vinyl flooring but I would like to put down a nice light wood coloured laminate flooring, although I'm debating about holding off on the flooring because I don't know if it will withstand a large dog constantly running on it!

Here is a tool on the Armstrong site where you can design your kitchen using different flooring and wall & cabinet colors. I've heard that laminate floors are good with pets, but maybe consider the vinyl plank also. You can order samples from here too. It's a good idea to put together a story board with all your choices.
http://www.armstrong.com/flooring/en-us/design-a-room.asp?darScene=14&shortCode=A6862&productCategory=