Did you think about using some colour , or maybe even timber , instead of grey and light grey and off-grey and greyish cream ? Hamptons ( apart from being a different building style ) is crisp white , high quality accessories and maybe a stronger grey or blue . If I wanted to get anywhere near a hamptons feel ( not even technically correct for Hamptons 'style' ) I'd go option 3 , BUT with a stronger roof vent , the door column in a high quality schist or similar stone , multiple paned windows , a cedar garage door ( or maybe crisp white with mid blue surround , but you'd have to carry the mid blue through to the front door and probably gutters and even highlights on an otherwise crisp white front fence ) . I know thats blunt , but there are whole suburbs that are variations of your design and colours , and they aren't in the Hamptons ( unless the Hamptons is a suburb of Newcastle or Adelaide ) .

red bricks with black and white looks very stylish so i would prefer gloss ironstone or white for the door with a brushed stainless steel handle

I would keep the paint as it is , at least initially , but like you and Larkspur Lane Design say , concentrate on the accessories and bring in some colour that way . Just one thing -- Linkspur mentioned cushions -- you didn't . I assume the couch is staying , its practical but it needs lifting , so pick your ( or the consensus ) favourite colour , and have fun with cushions -- say 4 or 5 bright yellow ones , and 4 or 5 yellow and white chevron ones ; or purple or green or red or burgundy or . . . . . . . heaps of them , some in solid , some in stripes or 2 tone or polka dot or chevron . The larger wall ( lounge and dining areas ) I'd wallpaper in something in the similar tones as your cushions , toned down a bit ( or contrasting ) . Basically , a feature wall , with a large $200 clock and maybe a couple of small black and white prints . Some art ( I like abstract ) -- a large one on one of the other lounge walls . Maybe a rug too -- subtle or bright , just not clashing . Then you could really double down . 'This end' of the servery I'd do in your chosen yellow or burgundy or whatever , and re-tile the kitchen in similar toned tiles -- the white 'splashback' ones do absolutely nothing style or colourwise IMO . Right now , the plants are the brightest points -- I love plants , but when they are the most noticable thing , that's a worry . Work with the white , beige and grey ( and the plants ) , but use colour to lift everything .

If you click on a Houzz photo, and then tap on More, you will see the company/pro attached to the project. You can then contact them for specific tile names. Otherwise if it more general info re tile type or pattern layout, then something like Google can help with that.