Help me learn about coffee and tea

I've never been a coffee or a tea drinker.   I always laugh that I have plenty of other vices -- as I do like beer and the hard stuff, I like to gamble, I enjoy driving fast -- that I've never picked this one up.  I was always a soda drinker, to the point of a bit of insanity.   In college, I never picked up the coffee habit, but kept pounding soda.

The first time I lost weight, gearing up for my wedding, I switched from "regular" to "unleaded", moving to Diet drinks as part of the calorie management solution.   I did Weight Watchers, and it worked really well for me, and I was able to get down to a trim 175 for my wedding.   Sharon even thought it was too much weight loss.

I put the weight back on over the past two years, and with a rather stern warning from my doctor at the beginning of the year, I was told not only did I need to take the weight off, but that watching my sugars and carbs was going to be part of my life.   Yay me.

Thus, I geared up and dropped Diet soda as well as the other changes to my diet, and I'm well on track to target weight.   (Beer is currently under a restriction, where I only drink it in the UK, because mixed drinks in the UK is a waste of time and money.)  

What this has done, however, is leave me in a spot where, besides water, there aren't good "on the go" drinks.   With sodas out, and juices containing a lot of sugar I'm trying to avoid, and sports drinks off the table for calories reasons, I need to find myself something I can have.

Coffee and tea are things I've just not had the taste for, but I suspect it's because it's something I don't understand more than something I won't like.  For example, I didn't always like beer, and still don't like ALL beers (India Pale Ales just don't do it for me), there are beers I like and ones I don't like.   I feel like with this wealth of types of coffee and teas out there, there have to be ones I'd like!

But where to start is the bigger question.   I hear a lot of "go into a coffee shop and try things", but what to try?  When you don't know what things are, this isn't helping much.   I can't be adding tons of sugar to things either, as that defeats the purpose.

My preferences:

I like sweet things, and always have.  Of course, I'm on a sugar restricted diet, so no cheating and adding sugar.
Carb management is important, so watching those is important.

What to try?

I know there are a ton of coffee and tea drinkers out there -- how to best tackle this?