Yep, it looks like you bought some Bari strings. As you may already know, ukeleles come in different sizes. The bigger ukes ('yukes' as we like to call em' here in Hawaii, not to be confused with Alaskan Yukons) such as tenors and baritones typically use the larger gauges. If you use bigger gauge strings on a concert/standard size ukulele, I'd imagine the tone to be very mellow, if not dull. You may wish to reference d'addarios website for their recommended string gauges. A classical guitar steel-wound nylon "G" string (not an article of lingerie) is commonly used on tenors and baritones. And in that case the G-string (hehe) will be lower than the C. [Note: G-strings are very common here in Hawaii too, especially at the local Nightclubs and beaches.]
As for tuning the GCEA tuning is standard tuning. I've never played a uke with A-D-F#-B tuning. All of the tenors and bari's I have played were tuned a la Giant Cockroaches method as mentioned by BlindCowboy. That's a good way of remembering hehe.

We have many giant cockroaches here. Though not as large as Madagascar hissing cockroaches, the big roaches we have here FLY! Scary stuff.

The ADF#B tuning is more of a classical/concert tuning.
Additional info...hmm... well playing uke is like playing guitar with a capo on the 5th fret minus the "E" and "A" strings. BlindCowboy makes a good point on how a "G" chord on uke is the same formation of a "D" chord on guitar. If you look at playing a uke with the giant cockroach tuning as playing guitar with capo 5, minus strings 5+6 you practically don't have to learn any new finger/chord positions.
Ukulele trivial info -- ukeleles were brought to Hawaii by Portugese immigrant settlers. Hawaiians referred to the stringed instrument as "ukulele" when they saw the Portugese cowboys vigorously playing. Ukulele translates into "jumping fleas", "uku" meaning lice/fleas and "lele" to jump. The Portugese fingers moving rapidly across the strings looked like jumping fleas. Funny how things get named huh?
As for tuning machines, BlindCowboy makes another good point on how friction tuners lose pitch constantly, especially on cheap ukes. I recommend saving your money and getting a decent uke. And/or until then you can just practice on guitar capo 5.
Here are some brands you may wish to look into. I know there are others, but I admit I am biased toward Ukes made in Hawaii, with the exception of the Ovation/Applause models--these are quite common here. Ovation/Applause makes an acoustic-electric soprano uke for around $179. Kamaka is the brand to get here in Hawaii, unfortunately these bad boys fetch a pretty penny $300-500 and up depending on what you get. Sonny D. and Bacani are other brands I have played, they are well made, play and sound great. Sonny D. goes for about the same as Kamakas, Bacani's are a good value selling for a couple hundred bucks cheaper if you can find one.
If you want to hear some different styles of ukulele playing look into Israel (IZ) Kamakawiwo`ole - traditional Hawaiian; Ka'au Crater Boyz - Contemporary Hawaiian/Folk; Jake Shimabukuro - Jazz/Rock/Classical Fusion.
Aloha!