Rarely do you see people riding 'stock' BMX bikes - the bikes are as individual as the riders. Typically 'mummy' buys a 'stock' BMX and over time it gets more evolved, e.g. a frame with a longer top tube and fancy, bespoke parts.
In the UK 'Mongoose' branded bikes are probably the best stocked and even then it is rare to find a bike shop with more than a few of the models, chosen to meet price points rather than due to the virtues of the bikes. Invariably you get tyres for the riding you describe with soft rubber rather than chunky tyres of a harder compound for the dirt track.
Coming from a cycling background you might find it hard to be on a bike that has just the one fairly weak rear U-brake or sidepull (or no brakes at all). Therefore you may want to have a look at the almost-mainstream models that come with both brakes. These come with a 'rotor' in the headset so the bars can be turned 360. These bikes usually come with 'stump pegs' and typically weigh several metric tonnes. You can obviously take the 'stump pegs' off as well as the brake/rotor to get the weight down.
Only the department store BMX bikes come with wheels that are less than robust. Most BMX come with 36 spoke wheels and that is a lot of spokes on a 20" wheel.
The chainring size is something to look out for. Most of today's BMX bikes have a ridiculously small chainring. The sprocket is also absurdly small so the gearing is the same as normal. You save weight and have higher clearance with the small/small gearing. Stay away from older models with the big chainring.
As for where you are now, you can go the traditional route of getting an available bike, such as a Mongoose freestyle model, to pimp it over time to suit your riding style. Alternatively you can buy a frame/bike of beauty such as a bike by 'We The People' and, even if you don't take up riding it too often, you will have a beautiful bike to look at.
As with all things cycling it is the rider and not the bike. Some of those bikes that get thrown around in a gravity defying way by the experts are unbelievably heavy, probably heavier than a typical MTB or a fully equipped hybrid. Bear this in mind when you go to a LBS that stocks BMX or get something online.