I would be concerned about siting more than anything: you want something you can access easily (where is your sliding door?); where is the regular sunshine?; what is the slope for drainage?
We *did* build an outdoor kitchen. We had sticker shock when we saw them in the BBQ stores here - cost was ~ $2k per linear foot! So DH decided to build one for us, and it's gorgeous.
It's about 15' long, topped with granite. The left most section is ~ 2' of countertop; then we have an XLarge Big Green Egg, on a recessed and dropped plinth, also topped with fireproof granite. It has two flat drawers underneath it, for utensils. Then another 3' of granite, with a set of three drawers (wood chips, more utensils, firestarters, etc.). Then a gas grill "head", with two doors underneath it for bulky stuff, like charcoal. And then another 2' of granite counter, with an outdoor fridge underneath it.
We had a frame built for us out of aluminum (rust-proof); then DH added hardy board, and a spray on stucco, with toe kick lighting and electrical outlets. He then topped it with 1.5" of plywood, and had a granite installer install the custom countertop. Total cost was ~ $6k, and took about 6 months to build.
We also have had great luck using a PVC decking (not Trex, which has had issues with delamination). We used Azek, and DH loved it. It's expensive, but durable, and the color is dyed into it with UV protectors, so no color splotching. Colors are limited, and he had to customize some of the materials to make a handrailing for stairs as well as a gate (at the time, those were not pre-fab options; they may be, now).
Our deck is very large, and having a huge patio umbrella has been sufficient; we didn't want a pergola, as it intrudes on the feeling of spaciousness we like when outdoors. We also had to look long and hard for a patio table that didn't have an undercarriage of supports, placed just right for me to bark my knees on every time I scooted my chair in. ;)
DH also added a firepit to the deck; he removed the wood in an 8x8' section, and built a tray of hardyboard, thinset, and tile with grout; to create an area that is safe for small fires. We then just have a steel standalone firepit, relatively inexpensive.
For lighting, my big tip is put them on dimmers. Nothing worse than a lovely summer evening with a 200 watt lightbulb blaring out into the bay....