I don't play uke, just cavaquinho, so I'm not going to comment specifically on technique, but as a samba nut and percussionist I can fill in some of the background where rhythm stuff is concerned at least.
In bossa nova the guitar holds together the rhythm and samba feel. The pulse of samba has a higher bass tone on the 1 and 3, and a lower tone on the 2 and 4, if you are counting in 4/4. The thumb usually alternates, on a guitar or I suppose a uke, between the top and 2nd to top stings to provide this pulse. Apparently the low and high note are usually a 5th apart, but you can double up and just replay the high or the low you just used if you can't get to the 5th from the chord you're on.
Some of the most important rhythms that you'll commonly come across the are the bossa clave and teleco-teco.
bossa clave
x--x --x- --x- -x-- (where each group of 4 is 4 1/16 notes)... similar to the 3/2 son clave with the last beat shifted forward one 1/16 note.
Teleco-teco
-x-x --x- x-x- x--x
When you loop this it will actually sound like the pattern starts on the "a" of the fourth beat, since it misses the one. This one is extremely common in Samba of all kinds, and is indespensible... and unfortunately a little hard to pin down without hearing it. There are often additional notes added or deleted from this... the upshot is that the rhythms are more of a feel that the music should have, and can be suggested by playing around them. Samba is really rhythmically complex and bossa goes even farther and takes more liberties with the basic rhythms.
I'm not at all familiar with the chord progressions but they seem to be the super complex jazz 9th and 7th and weird stuff like that... Have fun with that
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Here's some youtube guitar videos I just found on a bossa rhythm, you can probably skip the first half of each where he shows all the guitar chords and just note the progression and figure the best uke voicings out. The rhythm in the the second one is a variation on the teleco-teco, but it's hard to make out.
Something I think is important to note: the guy in the video says that bossa is not swung... which is true in the sense that the 1/8th notes are not swung in the traditional american jazz manner. Samba has it's own swing that is in the 1/16th notes, the e is shifted a bit towards the &, and the a is maybe shifted a bit farther away from the & towards the 1. The upshot is that it has a feel that is hard for Americans to pick up, but the 1/8 notes end up being in time basically, so you probably don't have to worry about that too much at first. When you get into soloing or deeper into the rhythms, take the time to listen to a bunch of bossa and samba to begin to understand the feel and the samba swing.
#1
http://www.youtube.com/watch?v=Rl8J2AcwngA
#2
http://www.youtube.com/watch?v=oCrcpulSZCU
You also might be intersted in checking out samba and pagode (a sub-genre of samba).
They both incorperate the cavaquinho, which is the steel stringed cousin of the uke, and have a lot of stumming. It's a lot of fun and would work well with the uke. If anyone is interested, pm me and maybe I'll through together a post of where to find stuff about other samba, which is not the easiest thing in the world without being able to read a little portuguese.