Brendel is a very good choice for a complete set, but he would not be my first choice for any single particular sonata -- not one. Good set to start with though, I think.
Gilels' incomplete cycle is fantastic.
Solomon's incomplete cycle is fantastic.
Bruce Hungerford's incomplete cycle is fantastic.
Gieseking's incomplete cycle is fantastic.
My favorite complete cycle is hands-down Kempff (mono), and I have not heard Annie Fischer's complete cycle, but some very experienced listeners inform me that hers may be the best ever recorded. I'm checking it out soon.
DON'T RELY ONE JUST ONE CYCLE. TRUST ME! If you're going to get a complete cycle, make sure you complement it with other recordings of the sonatas, because no cycle will have the best version of every sonata. I still say the first or third Brendel cycle is a good starting point, but GET OTHER RECORDINGS YOU MUST.
For the late sonatas, go for Pollini, Gieseking, Solomon, Hungerford, Schnabel.
For middle period (i.e. Waldstein, Appassionata, Les Adieux, and those in between), check out Gilels, Richter, and Robert Casadesus (at least those that they recorded) -- and for Waldstein in particular, I am in love with Pollini's live DG release grouped with Opp. 22 and 26.
For early-middle (i.e. Op. 22 - Op. 31), I recommend Rubinstein, Kempff (mono), Barenboim (either cycle really), Solomon.
For early sonatas, I recommend Kovacevich, Pollini (recent DG CD with Opp. 10 and 13 -- humorless but elegant/powerful/astonishing playing), Hungerford, Solmon, and Kempff (mono).
I know you are looking for one cycle to start with, so go get Brendel (first or third cycle) or Richard Goode, or hell, even Ashkenazy's cycle is a great place to start -- but make sure you check out different recordings, starting with your favorite sonatas. Start with some of my recommendations, or ignore them completely and get rec's from someone else. But know that I have 2.53 GB of just Beethoven piano sonatas on my computer, and more recordings on CD, so I am an experienced listener and can give good advice regarding these sonatas.
Good luck!