re: Please tell me about your kitchen appliances ...

If you want a really nice luxurious look, and have good high btu burners, and good build design.
Not much will match the burner btu and burner spread of a Thermidor or Viking, but there are great higher end big name branded items. Pretty much any natural gas oven or anything natural gas can be changed to Propane. The igniters are usually designed for both, really just changing the regulators and intake line.
So your fuel should not be a problem, just the added expense of needing new parts added to it, or many times you can get the units already with the Propane components.

I would look at Kenmore Elite, GE Profile and even Whirlpool. Each makes some great looking units, and they do their job. I think their pricing is good for the quality level. On the Dishwasher, no mater what color the front panel, I would recommend a stainless steel inner tub.
Any particular features that you want? Things to avoid?
Pretty much internally they are the same from one to the other. The differences in most appliances is solely electronics and appearance and 'added features'.

(Except for the Korean, European and New Zealand (F/P) brands, which while nice and functionally superior I'm not sure the higher price is really worth it)