glad to hear you made a choice. i agree with pianowelch that you can learn the other two as well, later. they all seem to be very difficult, but maybe the brahms is easier to practice slow - and gradually faster. you have breaks in between the variations, too.
i learned this one on my own - all of book 1. this took about a half year - and then the rest of the year to speed it faster and faster. your progress will probably be faster than mine, considering #1 no teacher at the time #2 working at my own pace - around household stuff.
the first variation i found it easier to use 5and2 alternating with 4and1 in the rh. that's probably a given for most - but i can give you more (of my personal fingerings). in measure 17 and 18 in the l.h. you can use 5,4,2 on the a min. chord and E major chord. this leaves your 3,1 fingers for the alternating thirds.
i don't know if this is a good fingering, but in measure 19 in the lh i use 3,1 again on the last third a-c , so i can use 5,4,2 on the E major chord in the next measure.
in measure 29 i use 5,4,2 on the A major chord, and then 1,3 - 4,2 - and 3,5 on the last three thirds (b,d- a,c#- g,Bb) after this succession - i literally picked up my hand and replaced in in the new position. you will find after playing it over and over, it is quite easy.
the next passage (m30) i use 5,4,2 and then 1-2-1 and switch to finger 2 at the top of the next chord.
i love variation 5!!! it is really beautiful.