With all that green IMO you need some color I do not like the striped rug but the one with all the leaves is fun. Those sofas do not look comfy at all do they have cushions that you are not showing?Is that all that is on the deck? I would get some nice big pots filled with seasonal plants for sure . Can you post a pic of the deck with the house. Post here in a comment do not start another post .

Thanks. we do have some pots with plants. i will add a pic taken a few days ago as the weather is gloomy today the new furniture is where thw table is in the pic.. there will be a much smaller table where the sun loungers are. the funiture has integrated cushions ans is very comfortable.

Either of the florals for color.

Along with the rug, more string lights...the bigger ones. A colorful tablecloth. A nice garden wall sculpture on the house to the right of the door-metal sunburst type of thing for example. Colorful throw pillows. Hanging pots.

I’d start with cushions on the sofas.

https://www.jossandmain.com/outdoor/pdp/outdoor-sunbrella-seatback-cushion-j100000189.html

https://www.rugsusa.com/rugsusa/rugs/rugs-usa-bordered-solid-indooroutdoor/Light-Gray/200OWCH01A-P.html

Add color with accents and plants. I’d keep the furniture fresh and neutral

Everything about your yard and iron toned furntiture screams English Garden to me, so that's what I'd look for in an outdoor rug

https://society6.com/product/william-morrisart-nouveauvintage-pattern-floral-victorian-pattern_outdoor-rug

https://society6.com/product/william-morris-vintage-blackthorn-dark-green-1892_outdoor-rug?sku=s6-24354307p143a307v1072

https://society6.com/product/william-morris-antique-acanthus-floral_outdoor-rug?sku=s6-22561377p143a307v1072

It’s really a matter of taste and the direction you want to head in general. It’s easier to start off with a color and liking it enough when accessorizing. Next, decide on the design: florals, stripes, geometric patterns, solid, etc. Then begin a pattern search, as your choices were so different from each other, which makes choosing hard.

Personally, I prefer a less strong pattern (in any color) so that it doesn’t take over and easy to complement. Also, don’t forget once you add the accessories they will also have a big influence in how the deck feels.