As Bob said, I did this for a living until I retired a couple of years ago. Attached is a picture of one of our simpler designs.
Planning is one of the biggest components. If you want a sink, you'll have to have both water and drain. If you want an under-counter fridge, you'll need an outlet under the cabinet. If your grill has a rotisserie, you'll need an outlet above the cabinet.
We were never happy with any of the conventional ways of building an outdoor kitchen cabinet, so we invented our own. Wood will burn, rot and attract critters. Cement block is too heavy, too messy, and too thick -- takes up valuable storage space under the cabinet. Brick is fine, but it doesn't fit the Florida decor -- we built hundreds of cabinets, and not once did someone ask us for a brick look, even though brick would have been their first choice, up North.
Instead, what we did was fabricate a frame for the cabinet from welded square tubing aluminum. Once that frame was installed, we attached a "skin" of HardiPanel, a cementious exterior siding. Over that, we applied a veneer of whatever "look" the customer wanted. The attached picture has a stucco cabinet in a sand finish, with a granite counter top. It has a bar sink. refrigerator, and 2 stainless access doors for storage. The grill is a Dynasty, made by the folks who make kitchen ranges, etc. of the same name. They're one of the Maytag companies. It's a fairly high-end unit, costing about $2400 in this size. There are two bigger sizes that go up to about $3600 and $4800 (for the grill). This is fairly typical, but there are some units down in the $1,000 price range, but not in stainless. The lowest price stainless built-in grill that I could recommend would be about $1700.
The doors range from $200 to $400 each, depending on size, who makes them, etc. Sideburners are available. The fridge can be either high end or low end. A U-line or Marvel will set you back about $1500 or so, but are SS and rated for outdoor use. A Danby will cost about $250, have a SS door, probably not last as long as the high-end units, but you can buy 6 of them for the same price as the high end unit. Most sinks are standard bar sinks, $40 or so (plus faucet) from HD..
I almost forgot -- if you will be putting the grill under a porch roof, you will have to give serious thought to installing a hood. Some building codes require it. The hoods must be powerful -- about 300 CFM for each 20K BTU, with a 600 CFM minimum. We sold Vent-a-hood, which adds squirrel cage blowers @ 300 CFM each to get the desired amount. The hoods can easily cost as much as the grill, plus installation -- usually ducted through the roof or a back wall.
For your brick cabinet, the FireMagic grill folks have a pamphlet available that describes brick construction and would be a good starting point. Click
FireMagic, look at their grills, and email them requesting their brick construction pamphlet. It used to be on-line, but I couldn't find it this morning -- but, I'm at my new homesite, using a cell phone interface for the laptop, which is considerably slower than my usual cable connection, and I lose patience easily.
