There are many different styles to choose from and it can be confusing. Why not have a look at the rugs on Houzz [Floor rugs[(https://www.houzz.com.au/products/floor-rugs-prbr0-br~t_13167) and save the ones you like to an idea book? This will help you to identify what you like design & colour wise. I like your room and as jmm1837 said a traditional style will suit your decor. For some ideas to start with...

So I searched for navy exterior and had some blue and white American monstrosities turn up, but I've found some nuggets of perfection that I think you suit the exterior cladding. How about dark blue/navy? I think it would really suit the water front location and also highlight the great features about your home. You have a great green area in your front lawn, and blue and green together will really accentuate the area. Show us some photos of the end result!

Teal works really well with dark chocolate brown and beige (greeny blue teals with deep brown leather sofas or tables and caramel walls pop and yet are homely and comfortable) so a rug underneath the table and sofa to delineate that space with teal in it or all teal (I would go for a pattern as you have very neutral pieces the one from Kathy above with caramel and beige is perfect I think) could work -ditto curtains and cushions. Given the neutral pieces you could add pops of another colour depending on the teal tones you use. Also lighter turquoise tones that sort of layer with teal - its deeper cousin.... a turquoise ceramic (or other objects) with a toning teal one ( teal and turquoise can vary on the blue-green spectrum) and a lovely caramel coloured piece ( things work well together in 3's I find) all of varying heights shapes and some texture on at least 1 - would look great somewhere. Burnt orange (a more subtle tone than hot orange) can be a great and more adventurous addition as can khaki - just keep them subtle and mix it up. I have a great market bought cushion made from an old woollen tartan type blanket of aqua /turquoise, a light khaki and burnt orange with a caramel leather cross on it that looks so good on my dark brown leather sofa (sorry no photo on me).

Agree with above comments - large rug, darker colours to balance the beige. And I also think the art work is too small and too high. However if you are attached to these pieces they could be hung together on one wall, lower, maybe re-framed in similar frames to give them cohesion (black to match your new cushions?). This would create the effect of a larger art piece. (The centre of your art should be at average eye height - and in that room you are sitting so eye height is lower!)