Let's remember that we are talking about what to order with your boss. This is a unique and specific situation. I agree with most of what you two are saying (with the exception of ordering - or drinking - a "Cuba Libre," which just makes you sound like a moron and embarrasses the bartender and the people you're with). I was a bartender one summer and it was the hardest job I've ever had, although very fun.
I tended bar at a nice resort hotel that was also a fairly busy post-dinner spot. I saw a lot of business drinks and an order can actually get things off on a good/bad note. For instance: when people do not know what they want, their companion will often get fidgety and embarrassed. I've seen meetings when people will order a drink and then return it because it wasn't what they thought (OMG). A quick, confident order is best for business. As someone else mentioned, it is okay to ask for a beer/wine list, but keep the barrage of questions for when you're out with friends.
If you order a Manhattan or an Old Fashioned (or the others mentioned), it should be because you are familiar with the drink and its ingredients. If you order it to look cool, it'll backfire.
Never order a martini on business unless you know it is okay to get tipsy, and always, ALWAYS, order it in a rocks glass. Again, I am talking about business drinks. When you're out having fun, do whatever the hell you want.
Now, on to a personal disaster story of mine that happened when I was interviewing for a job. I had met with a company for three rounds of interviews and during the last interview - a panel - someone suggested that we go for drinks after. It was a late-afternoon interview with 5 people and there was a bar in the lobby of the building. Of course I agree, so we all walk down. Because I was the "guest," they looked to me to order first. I ordered a fairly strong local draft beer, and then everyone else proceeds to order something without alcohol. I couldn't figure out what was going on. I was like, "why suggest drinks if no one is going to drink," thinking it was some kind of odd test. So we all sit there, everyone is very uncomfortable, for like 15 minutes chatting and finally I just asked. We all laughed and everyone had their excuse (spin class, driving home, don't drink) and apparently it just happened that no one wanted to drink that night. I got the job and worked there for 7 years. The story got rehashed by my boss every year at the Christmas party (I started around Christmas) and the whole awkward situation ended up working in my favor...