Basic rule when arriving in foreign country where you don't speak the language or have never been before... get the hotel to pick you up. Simple. If you can afford the Grand Hyatt or St Regis, then the cost of an airport transfer is marginal, given the hassle saved.
When Sean arrived in BJ a few months ago, and was collected by Kerry Centre hotel car - they even met him at the plane jetway and whisked him through immigration. Marvellous.
Being driven to your hotel means you get your bearings faster, can relax and enjoy the view, not have to struggle getting to an ATM etc etc etc. By all means take taxis later.. but wait until you have got over jet lag.
To see the sights in central BJ, the underground/metro and a good map are all you need, as well as a pair of comfy shoes. Maybe a taxi or two depending on how much shopping I suppose !
As for day trip to Gt Wall, the last time we did this it was easy, we checked out the options in the hotel travel desk and went for a driver only (no guide) and had a great day out. Cost was about $70 i think, not sure as have thrown bill away ages ago. Just avoid Badaling, unless you like crowds and need to buy a few hundred more t-shirts.
Regarding the souvenir shop stopovers, I am sorry to say it does happen, but you can refuse to get out of the car you know. Or spend 10 mins there, just in case, then leave.
And yes, taxi drivers can often simply not read. This happens in a lot of countries, but commonly in China. Also, as you'll see BJ is changing, and fast. Construction is everywhere. Whole districts have been demolished. Place names in English sound nothing like their real names.
Simplest way to sort this out is walk to nearest hotel (or office complex) with a cab rank and get the doorman to direct him. Have a drink in their bar while you decide where to go next perhaps.. or keep your cellphone handy and call for directions.
Just don't call me, as my friend did, as if the taxi driver would understand me better.