Reddit mentions of Gourmet Gift Tea Set "Czar Nicholas II", 5 Flavors by Tea Nicholas

Bittersweet is easy! Many teas are naturally a little bitter, and there's a reason why it's common to add sugar (or honey). I'd stay away from the darker teas here, but a basic oolong tea is going to be light and a little bitter. I drink this one regularly, but there's plenty of other alternatives. Green teas are also going to be a good choice here, though I don't know them well. If you want something with a little extra body, try a Genmai Cha, which is a green tea with toasted rice added.

Fruity is also easy, but I may be the wrong person to ask here; the only fruity teas I get into tend to be tangy. That said, virtually any fruit or berry can be turned into a tea, and I'd wager all of them have. In my experience you can find fruit teas in two major categories, standard teas with fruit added and teas that are literally just fruit; the former generally include caffeine, the latter don't.

(Caffeine rule of thumb: black teas have caffeine, green teas have a little caffeine, if it doesn't actually have tea leaves in it, it contains no caffeine.)

Most tea vendors online have a "sample" option that gives you enough tea for half a dozen cups at a very low price. If you're just experimenting with teas, picking up half a dozen to a dozen samples is a pretty good way to start. I'm linking to Upton because I buy most of my teas from them and I know their samples are good - they often include a free sample or two in the box just for fun, in fact - but there's plenty of other good tea vendors online.

Finally, here's the tea snob in me; you know teabags? Teabags suck. They're more expensive and lower quality and have less variety. You get the absolute lowest-quality tea in them, pay a premium for the bag, and your options are sharply limited. I strongly recommend picking up a tea infuser which makes looseleaf teas both easy and convenient to brew. If you're just experimenting with teas and don't want to put out the money for the infuser, there's cheaper solutions, but IMO they're more awkward and annoying and also don't provide as good of a result if you're dealing with a tea that seriously rehydrates.

And note that looseleaf teas have to be kept in a reasonably airtight and opaque container. Most vendors will sell you teas either in a competently-made tea tin or at least a resealable pouch - everything Upton sells you will show up sensibly packed - but you can't always guarantee that. I bought this set a while back and the first thing I did was move them into resealable tea tins (sold by Upton, natch.)

Now you know more than you wanted to about tea :)