If considering wood you could get unfinished wood installed. Companies such as Wood Floor Accessories are a great supplier. Having it finished on site means a finish can be picked that works for your home. Each home has variables such as pets, different traffic and the owners desire to maintain the flooring or aversion to maintenance. Having wood finished on site has advantages. You can pick the highest quality product that works for your budget. The range of finishes available is quite wide. A professional company will try to understand your home and recommend the appropriate finish. They will also understand how easily the finish was can be renovated in the future. Amtico is an extremely robust product but being plastic, is just plastic flooring. It has its place, as does wood. In areas that have plenty of light surfaces, scratches show very easily on Amtico, Karndean etc. The manufacturers push a polishing maintenance product on consumers. However, this needs to be stripped and reapplied on a regular basis.

Is does seem that the lesser known brands of LVT are the same thickness and same warranty as the major brands- the difference seems to be the colour choice and size of marketing budget. So as long as you like the colour choice with another brand then I think the cost saving is worth having. Separately the issue with herringbone over an expansive area is making the pattern meet up- generally a competent fitter will have no problems- I wonder if the issue is that you aren’t actually looking at LVT but instead floating floors (click together floors as opposed to stick down to the screed). Floating floors need to expand and over a large sized area can need an expansion strip adding which looks fine if you can add it to a doorway but looks odd in the middle of a large room.

Rinked, I also considered that, but the table and chairs would block access to the back garden. The front extension would significantly block most of the south-facing light in the living area, the back double doors, are north-facing so they don't bring in any light. So while I agree that you need some sort of entrance into the home, The front extension is a mistake in my opinion. In regards to the comment of keeping the passage, yes it's good to have, however, soo many people who live in terrace houses don't have that option and I don't see that as a significant issue.

I'd also be inclined to swap them as Jonathan suggested. Check fire regulations, as perhaps you do need to rotate the stairs to allow an open kitchen. (I'm in the Netherlands so can't advise on these.)